Convexity and Monotonicity Involving the Complete Elliptic Integral of the First Kind
Let K r be the complete elliptic integral of the first kind defined on 0 , 1 . By virtue of the auxiliary function H f , g = f ′ / g ′ g - f , we prove that the function Q p x = ln p / 1 - x K x is strictly convex on 0 , 1 if and only if 0 < p ≤ 4 , thus answering a conjecture. Moreover, we compl...
Uloženo v:
| Vydáno v: | Resultate der Mathematik Ročník 78; číslo 1; s. 29 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.02.2023
Springer Nature B.V |
| Témata: | |
| ISSN: | 1422-6383, 1420-9012 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Let
K
r
be the complete elliptic integral of the first kind defined on
0
,
1
. By virtue of the auxiliary function
H
f
,
g
=
f
′
/
g
′
g
-
f
, we prove that the function
Q
p
x
=
ln
p
/
1
-
x
K
x
is strictly convex on
0
,
1
if and only if
0
<
p
≤
4
, thus answering a conjecture. Moreover, we completely described the monotonicity of
Q
p
x
on
0
,
1
for different
p
∈
0
,
∞
. |
|---|---|
| AbstractList | Let Kr be the complete elliptic integral of the first kind defined on 0,1. By virtue of the auxiliary function Hf,g=f′/g′g-f, we prove that the function Qpx=lnp/1-xKxis strictly convex on 0,1 if and only if 0<p≤4, thus answering a conjecture. Moreover, we completely described the monotonicity of Qpx on 0,1 for different p∈0,∞. Let K r be the complete elliptic integral of the first kind defined on 0 , 1 . By virtue of the auxiliary function H f , g = f ′ / g ′ g - f , we prove that the function Q p x = ln p / 1 - x K x is strictly convex on 0 , 1 if and only if 0 < p ≤ 4 , thus answering a conjecture. Moreover, we completely described the monotonicity of Q p x on 0 , 1 for different p ∈ 0 , ∞ . |
| ArticleNumber | 29 |
| Author | Tian, Jing-Feng Yang, Zhen-Hang |
| Author_xml | – sequence: 1 givenname: Jing-Feng surname: Tian fullname: Tian, Jing-Feng organization: Department of Mathematics and Physics, North China Electric Power University – sequence: 2 givenname: Zhen-Hang surname: Yang fullname: Yang, Zhen-Hang email: zhyang_ncepu@163.com organization: Department of Science and Technology, State Grid Zhejiang Electric Power Company Research Institute |
| BookMark | eNp9kE1PAjEQhhuDiYD-AU-beK72Y9ndHg0BJWK8yLnpdmexZGnXthD49y6siYkHTjOZeZ_5eEdoYJ0FhO4peaSE5E-BEMImmDCGCc2FwIcrNKQpI1gQygbnnOGMF_wGjULYEDJhjLIhWk2d3cPBxGOibJW8O-uis0afCgu7d83e2HUSvyCZum3bQIRk1jSmjUZ3_Qhrr5rE1WfF3PgQkzdjq1t0XasmwN1vHKPVfPY5fcXLj5fF9HmJNaci4rwsuGJ5nWZFprJalwCl0LoQoECIEgjNqC40VIoqlVZlrZkCyEtNcpELSvgYPfRzW---dxCi3Lidt91Kydmkezflgneqoldp70LwUMvuPRWNs9Er00hK5MlE2ZsoOxPl2UR56FD2D2292Sp_vAzxHgqd2K7B_111gfoByOaI9A |
| CitedBy_id | crossref_primary_10_1017_S0013091524000440 crossref_primary_10_1515_ms_2025_0060 crossref_primary_10_1007_s10986_024_09644_0 crossref_primary_10_1007_s13398_023_01465_z |
| Cites_doi | 10.1137/0527044 10.2298/AADM190924020W 10.1186/s13660-018-1687-x 10.1007/s00025-021-01538-8 10.3934/math.2020466 10.1007/s00025-022-01641-4 10.1080/10652469.2020.1738423 10.1017/S0305004198002692 10.1016/j.jmaa.2018.10.034 10.1137/S0036141096310491 10.1137/0521029 10.1007/978-3-642-65138-0 10.1016/j.jmaa.2019.02.018 10.7153/jmi-2021-15-87 10.1007/s00009-017-0971-1 10.1016/j.jmaa.2022.126609 10.1137/0523025 10.1137/0516080 10.1186/1029-242X-2014-192 10.1016/j.cam.2004.02.009 10.1186/s13660-016-0988-1 10.1007/s40315-020-00352-7 10.7153/jmi-2021-15-50 10.1016/j.jmaa.2015.03.043 10.2298/AADM171015001Y 10.1016/j.jmaa.2021.125889 10.1007/s11139-018-0061-4 10.1007/s13163-022-00439-w 10.1002/zamm.19940740220 10.1007/s13398-021-01021-7 10.1007/s13398-020-00992-3 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. |
| DBID | AAYXX CITATION 7XB 8FE 8FG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- M2P P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS Q9U |
| DOI | 10.1007/s00025-022-01799-x |
| DatabaseName | CrossRef ProQuest Central (purchase pre-March 2016) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Korea ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Science Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China ProQuest Central Basic |
| DatabaseTitle | CrossRef Advanced Technologies & Aerospace Collection Computer Science Database ProQuest Central Student Technology Collection ProQuest Central Basic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Science Journals ProQuest Computer Science Collection ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Advanced Technologies & Aerospace Collection |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central Database Suite (ProQuest) url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1420-9012 |
| ExternalDocumentID | 10_1007_s00025_022_01799_x |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 203 29P 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 78A 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAEWM AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HLICF HMJXF HQYDN HRMNR HVGLF HZ~ IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM P2P P9R PF0 PT4 QOS R89 R9I RHV RIG ROL RPX RSV S16 S1Z S27 S3B SAP SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR YNT Z45 ZMTXR ZWQNP ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP ARAPS ATHPR AYFIA AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ K7- M2P PHGZM PHGZT PQGLB 7XB 8FE 8FG JQ2 P62 PKEHL PQEST PQQKQ PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c319t-7b83a27f4686a6fcbeeb9cc89eae99be0161c8ceda1aa4dbfc2aee7bc07979103 |
| IEDL.DBID | M2P |
| ISICitedReferencesCount | 10 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000890291300003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1422-6383 |
| IngestDate | Mon Oct 06 17:10:28 EDT 2025 Sat Nov 29 03:47:26 EST 2025 Tue Nov 18 22:11:21 EST 2025 Fri Feb 21 02:46:19 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | inequality Primary 33C05 26A51 Secondary 39B62 hypergeometric function convexity Complete elliptic integral of the first kind |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-7b83a27f4686a6fcbeeb9cc89eae99be0161c8ceda1aa4dbfc2aee7bc07979103 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3256384393 |
| PQPubID | 7435734 |
| ParticipantIDs | proquest_journals_3256384393 crossref_citationtrail_10_1007_s00025_022_01799_x crossref_primary_10_1007_s00025_022_01799_x springer_journals_10_1007_s00025_022_01799_x |
| PublicationCentury | 2000 |
| PublicationDate | 20230200 2023-02-00 20230201 |
| PublicationDateYYYYMMDD | 2023-02-01 |
| PublicationDate_xml | – month: 2 year: 2023 text: 20230200 |
| PublicationDecade | 2020 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham – name: Heidelberg |
| PublicationSubtitle | Resultate der Mathematik |
| PublicationTitle | Resultate der Mathematik |
| PublicationTitleAbbrev | Results Math |
| PublicationYear | 2023 |
| Publisher | Springer International Publishing Springer Nature B.V |
| Publisher_xml | – name: Springer International Publishing – name: Springer Nature B.V |
| References | Tian, Yang (CR18) 2022; 77 Yang, Qian, Zhang, Chu (CR33) 2020; 23 Zhao, Wang, Chu (CR41) 2021; 15 Yang, Tian (CR25) 2019; 470 Yang, Tian (CR24) 2022; 42 Biernacki, Krzyz (CR6) 1955; 9 Gaunt (CR10) 2022; 77 Yang, Tian (CR36) 2019; 13 Richards, Smith (CR16) 2020; 32 CR19 Yang, Chu (CR28) 2022; 508 Yang, Chu (CR29) 2017; 20 Qiu, Vamanamurthy, Vuorinen (CR15) 1998; 29 Yang, Chu, Wang (CR31) 2015; 428 Qiu, Ma, Chu (CR13) 2019; 474 CR11 Yang, Tian (CR37) 2021; 15 Yang, Qian, Chu (CR32) 2018; 21 Yang, Tian (CR35) 2019; 48 Tian, Ha, Xing (CR17) 2020; 5 Yang, Song, Chu (CR34) 2014; 2014 Petrović (CR12) 1932; 1 Wang, Zhang, Chu (CR23) 2019; 39 Chen, Zhao (CR9) 2022; 116 Carlson, Guatafson (CR8) 1985; 16 Wang, Chu, Zhang (CR22) 2019; 22 Yang, Tian (CR38) 2022 Yang, Zheng (CR39) 2017; 14 Yang, Chu (CR30) 2016; 2016 Alzer (CR1) 1998; 124 Wang, Chu, Song (CR21) 2016; 276 Alzer, Qiu (CR2) 2004; 172 Wang, Chu, Li, Chu (CR20) 2020; 14 CR27 Anderson, Vamanamurthy, Vuorinen (CR4) 1990; 21 Byrd, Friedman (CR7) 1971 CR42 Alzer, Richards (CR3) 2020; 31 Yang, Tian (CR26) 2023; 517 Qiu, Vamanamurthy (CR14) 1996; 27 Zhao, He, Chu (CR40) 2021; 21 Anderson, Vamanamurthy, Vuorinen (CR5) 1992; 23 Zhu (CR43) 2018; 2018 Z-H Yang (1799_CR29) 2017; 20 Z-H Yang (1799_CR33) 2020; 23 S-L Qiu (1799_CR13) 2019; 474 PF Byrd (1799_CR7) 1971 GD Anderson (1799_CR5) 1992; 23 M Petrović (1799_CR12) 1932; 1 H Alzer (1799_CR3) 2020; 31 M-K Wang (1799_CR21) 2016; 276 Z Yang (1799_CR25) 2019; 470 1799_CR27 Z-H Yang (1799_CR39) 2017; 14 Z-H Yang (1799_CR37) 2021; 15 Z-H Yang (1799_CR28) 2022; 508 Z-H Yang (1799_CR30) 2016; 2016 Z-H Yang (1799_CR34) 2014; 2014 Z Yang (1799_CR24) 2022; 42 1799_CR42 S-L Qiu (1799_CR15) 1998; 29 Z-H Yang (1799_CR36) 2019; 13 M-K Wang (1799_CR20) 2020; 14 H Alzer (1799_CR2) 2004; 172 L Zhu (1799_CR43) 2018; 2018 H Alzer (1799_CR1) 1998; 124 RE Gaunt (1799_CR10) 2022; 77 S-L Qiu (1799_CR14) 1996; 27 Z-H Yang (1799_CR35) 2019; 48 Z-H Yang (1799_CR38) 2022 J-F Tian (1799_CR17) 2020; 5 1799_CR19 Z-H Yang (1799_CR32) 2018; 21 GD Anderson (1799_CR4) 1990; 21 M-K Wang (1799_CR23) 2019; 39 J-F Tian (1799_CR18) 2022; 77 BC Carlson (1799_CR8) 1985; 16 T-H Zhao (1799_CR41) 2021; 15 1799_CR11 M-K Wang (1799_CR22) 2019; 22 M Biernacki (1799_CR6) 1955; 9 KC Richards (1799_CR16) 2020; 32 Z Yang (1799_CR26) 2023; 517 Z-H Yang (1799_CR31) 2015; 428 Y-J Chen (1799_CR9) 2022; 116 T-H Zhao (1799_CR40) 2021; 21 |
| References_xml | – volume: 27 start-page: 823 issue: 3 year: 1996 end-page: 834 ident: CR14 article-title: Sharp estimates for complete elliptic integrals publication-title: SIAM J. Math. Anal. doi: 10.1137/0527044 – volume: 14 start-page: 255 issue: 1 year: 2020 end-page: 271 ident: CR20 article-title: Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind publication-title: Appl. Anal. Discrete Math. doi: 10.2298/AADM190924020W – volume: 2018 start-page: 94, 14 year: 2018 ident: CR43 article-title: On Frame’s inequalities publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1687-x – volume: 77 start-page: 1, 16 year: 2022 ident: CR10 article-title: Functional inequalities and monotonicity results for modified Lommel functions of the first kind publication-title: Results Math. doi: 10.1007/s00025-021-01538-8 – volume: 5 start-page: 7285 issue: 6 year: 2020 end-page: 7300 ident: CR17 article-title: Properties of the power-mean and their applications publication-title: AIMS Math. doi: 10.3934/math.2020466 – volume: 20 start-page: 729 issue: 3 year: 2017 end-page: 735 ident: CR29 article-title: A monotonicity property involving the generalized elliptic integrals of the first kind publication-title: Math. Inequal. Appl. – volume: 77 start-page: 109, 19 issue: 3 year: 2022 ident: CR18 article-title: Several absolutely monotonic functions related to the complete elliptic integral of the first kind publication-title: Results Math. doi: 10.1007/s00025-022-01641-4 – volume: 31 start-page: 758 issue: 9 year: 2020 end-page: 768 ident: CR3 article-title: A concavity property of the complete elliptic integral of the first kind publication-title: Int. Transf. Spec. Funct. doi: 10.1080/10652469.2020.1738423 – volume: 23 start-page: 77 issue: 1 year: 2020 end-page: 93 ident: CR33 article-title: Notes on the complete elliptic integral of the first kind publication-title: Math. Inequal. Appl. – volume: 9 start-page: 135 year: 1955 end-page: 147 ident: CR6 article-title: On the monotonicity of certain functionals in the theory of analytic functions publication-title: Ann. Univ. Mariae Curie-Sklodowska – volume: 22 start-page: 601 issue: 2 year: 2019 end-page: 617 ident: CR22 article-title: Monotonicity and inequalities involving zero-balanced hypergeometric function publication-title: Math. Inequal. Appl. – volume: 124 start-page: 309 issue: 2 year: 1998 end-page: 314 ident: CR1 article-title: Sharp inequalities for the complete elliptic integral of the first kind publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004198002692 – volume: 276 start-page: 44 year: 2016 end-page: 60 ident: CR21 article-title: Asymptotical formulas for Gaussian and generalized hypergeometric functions publication-title: Appl. Math. Comput. – volume: 470 start-page: 821 year: 2019 end-page: 845 ident: CR25 article-title: Monotonicity rules for the ratio of two Laplace transforms with applications publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2018.10.034 – volume: 29 start-page: 1224 issue: 5 year: 1998 end-page: 1237 ident: CR15 article-title: Some inequalities for the growth of elliptic integrals publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141096310491 – volume: 21 start-page: 536 year: 1990 end-page: 549 ident: CR4 article-title: Functional inequalities for complete elliptic integrals and their ratios publication-title: SIAM J. Math. Anal. doi: 10.1137/0521029 – ident: CR27 – ident: CR42 – volume: 1 start-page: 149 year: 1932 end-page: 156 ident: CR12 article-title: Sur une équation fonctionnelle publication-title: Publ. Math. Univ. Belgrade – volume: 32 start-page: 1 issue: 3 year: 2020 end-page: 13 ident: CR16 article-title: A concavity property of generalized complete elliptic integrals publication-title: Int. Transf. Spec. Funct. – ident: CR19 – year: 1971 ident: CR7 publication-title: Handbook of Elliptic Integrals for Engineers and Scientists doi: 10.1007/978-3-642-65138-0 – volume: 474 start-page: 1306 issue: 2 year: 2019 end-page: 1337 ident: CR13 article-title: Sharp Landen transformation inequalities for hypergeometric functions, with applications publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2019.02.018 – volume: 15 start-page: 1299 issue: 3 year: 2021 end-page: 1310 ident: CR37 article-title: Absolutely monotonic functions involving the complete elliptic integrals of the first kind with applications publication-title: J. Math. Inequal. doi: 10.7153/jmi-2021-15-87 – volume: 14 start-page: 169, 22 year: 2017 ident: CR39 article-title: Sharp bounds for the ratio of modified Bessel functions publication-title: Mediterr. J. Math. doi: 10.1007/s00009-017-0971-1 – volume: 517 start-page: 126609, 20 issue: 1 year: 2023 ident: CR26 article-title: Monotonicity results involving the zeta function with applications publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2022.126609 – volume: 23 start-page: 512 issue: 2 year: 1992 end-page: 524 ident: CR5 article-title: Functional inequalities for hypergeometric functions and complete elliptic integrals publication-title: SIAM J. Math. Anal. doi: 10.1137/0523025 – volume: 16 start-page: 1072 issue: 5 year: 1985 end-page: 1092 ident: CR8 article-title: Asymptotic expansion of the first elliptic integral publication-title: SIAM J. Math. Anal. doi: 10.1137/0516080 – ident: CR11 – volume: 2014 start-page: 192, 13 year: 2014 ident: CR34 article-title: Sharp bounds for the arithmetic-geometric mean publication-title: J. Inequal. Appl. doi: 10.1186/1029-242X-2014-192 – volume: 172 start-page: 289 year: 2004 end-page: 312 ident: CR2 article-title: Monotonicity theorems and inequalities for the complete elliptic integrals publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.02.009 – volume: 39 start-page: 1440 issue: 5 year: 2019 end-page: 1450 ident: CR23 article-title: Monotonicity, convexity and inequalities involving the generalized elliptic integrals publication-title: Acta Math. Sci. Ser. B (Engl. Ed.) – volume: 42 start-page: 847 issue: 3 year: 2022 end-page: 864 ident: CR24 article-title: Absolute monotonicity involving the complete elliptic integrals of the first kind with applications publication-title: Acta Math. Sci. Ser. B (Engl. Ed.) – volume: 2016 start-page: 40, 21 year: 2016 ident: CR30 article-title: On approximating the modified Bessel function of the first kind and Toader-Qi mean publication-title: J. Inequal. Appl. doi: 10.1186/s13660-016-0988-1 – volume: 21 start-page: 413 year: 2021 end-page: 426 ident: CR40 article-title: Sharp bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals publication-title: Comput. Methods Funct. Theory doi: 10.1007/s40315-020-00352-7 – volume: 15 start-page: 701 issue: 2 year: 2021 end-page: 724 ident: CR41 article-title: Concavity and bounds involving generalized elliptic integral of the first kind publication-title: J. Math. Inequal. doi: 10.7153/jmi-2021-15-50 – volume: 428 start-page: 587 year: 2015 end-page: 604 ident: CR31 article-title: Monotonicity criterion for the quotient of power series with applications publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.03.043 – volume: 13 start-page: 240 year: 2019 end-page: 260 ident: CR36 article-title: Convexity and monotonicity for elliptic integrals of the first kind and applications publication-title: Appl. Anal. Discrete Math. doi: 10.2298/AADM171015001Y – volume: 116 start-page: 77, 21 issue: 2 year: 2022 ident: CR9 article-title: On the monotonicity and convexity for generalized elliptic integral of the first kind publication-title: Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM – volume: 508 start-page: 125889, 23 year: 2022 ident: CR28 article-title: Monotonicity and inequalities involving the modified Bessel functions publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2021.125889 – volume: 48 start-page: 91 year: 2019 end-page: 116 ident: CR35 article-title: Sharp inequalities for the generalized elliptic integrals of the first kind publication-title: Ramanujan J. doi: 10.1007/s11139-018-0061-4 – volume: 21 start-page: 1185 issue: 4 year: 2018 end-page: 1199 ident: CR32 article-title: Monotonicity properties and bounds involving the complete elliptic integrals of the first kind publication-title: Math. Inequal. Appl. – year: 2022 ident: CR38 article-title: Convexity of ratios of the modified Bessel functions of the first kind with applications publication-title: Rev. Mat. Complut. doi: 10.1007/s13163-022-00439-w – volume: 29 start-page: 1224 issue: 5 year: 1998 ident: 1799_CR15 publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141096310491 – volume: 48 start-page: 91 year: 2019 ident: 1799_CR35 publication-title: Ramanujan J. doi: 10.1007/s11139-018-0061-4 – volume: 428 start-page: 587 year: 2015 ident: 1799_CR31 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.03.043 – volume: 9 start-page: 135 year: 1955 ident: 1799_CR6 publication-title: Ann. Univ. Mariae Curie-Sklodowska – volume-title: Handbook of Elliptic Integrals for Engineers and Scientists year: 1971 ident: 1799_CR7 doi: 10.1007/978-3-642-65138-0 – volume: 21 start-page: 536 year: 1990 ident: 1799_CR4 publication-title: SIAM J. Math. Anal. doi: 10.1137/0521029 – ident: 1799_CR11 doi: 10.1002/zamm.19940740220 – volume: 124 start-page: 309 issue: 2 year: 1998 ident: 1799_CR1 publication-title: Math. Proc. Camb. Phil. Soc. doi: 10.1017/S0305004198002692 – volume: 15 start-page: 1299 issue: 3 year: 2021 ident: 1799_CR37 publication-title: J. Math. Inequal. doi: 10.7153/jmi-2021-15-87 – volume: 22 start-page: 601 issue: 2 year: 2019 ident: 1799_CR22 publication-title: Math. Inequal. Appl. – volume: 1 start-page: 149 year: 1932 ident: 1799_CR12 publication-title: Publ. Math. Univ. Belgrade – volume: 15 start-page: 701 issue: 2 year: 2021 ident: 1799_CR41 publication-title: J. Math. Inequal. doi: 10.7153/jmi-2021-15-50 – volume: 16 start-page: 1072 issue: 5 year: 1985 ident: 1799_CR8 publication-title: SIAM J. Math. Anal. doi: 10.1137/0516080 – volume: 276 start-page: 44 year: 2016 ident: 1799_CR21 publication-title: Appl. Math. Comput. – volume: 474 start-page: 1306 issue: 2 year: 2019 ident: 1799_CR13 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2019.02.018 – volume: 21 start-page: 1185 issue: 4 year: 2018 ident: 1799_CR32 publication-title: Math. Inequal. Appl. – year: 2022 ident: 1799_CR38 publication-title: Rev. Mat. Complut. doi: 10.1007/s13163-022-00439-w – volume: 31 start-page: 758 issue: 9 year: 2020 ident: 1799_CR3 publication-title: Int. Transf. Spec. Funct. doi: 10.1080/10652469.2020.1738423 – volume: 5 start-page: 7285 issue: 6 year: 2020 ident: 1799_CR17 publication-title: AIMS Math. doi: 10.3934/math.2020466 – volume: 42 start-page: 847 issue: 3 year: 2022 ident: 1799_CR24 publication-title: Acta Math. Sci. Ser. B (Engl. Ed.) – ident: 1799_CR27 – volume: 2014 start-page: 192, 13 year: 2014 ident: 1799_CR34 publication-title: J. Inequal. Appl. doi: 10.1186/1029-242X-2014-192 – volume: 32 start-page: 1 issue: 3 year: 2020 ident: 1799_CR16 publication-title: Int. Transf. Spec. Funct. – volume: 14 start-page: 169, 22 year: 2017 ident: 1799_CR39 publication-title: Mediterr. J. Math. doi: 10.1007/s00009-017-0971-1 – volume: 172 start-page: 289 year: 2004 ident: 1799_CR2 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.02.009 – volume: 39 start-page: 1440 issue: 5 year: 2019 ident: 1799_CR23 publication-title: Acta Math. Sci. Ser. B (Engl. Ed.) – volume: 470 start-page: 821 year: 2019 ident: 1799_CR25 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2018.10.034 – volume: 77 start-page: 1, 16 year: 2022 ident: 1799_CR10 publication-title: Results Math. doi: 10.1007/s00025-021-01538-8 – volume: 77 start-page: 109, 19 issue: 3 year: 2022 ident: 1799_CR18 publication-title: Results Math. doi: 10.1007/s00025-022-01641-4 – volume: 20 start-page: 729 issue: 3 year: 2017 ident: 1799_CR29 publication-title: Math. Inequal. Appl. – volume: 2018 start-page: 94, 14 year: 2018 ident: 1799_CR43 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-018-1687-x – volume: 517 start-page: 126609, 20 issue: 1 year: 2023 ident: 1799_CR26 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2022.126609 – volume: 2016 start-page: 40, 21 year: 2016 ident: 1799_CR30 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-016-0988-1 – volume: 116 start-page: 77, 21 issue: 2 year: 2022 ident: 1799_CR9 publication-title: Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM – ident: 1799_CR19 doi: 10.1007/s13398-021-01021-7 – volume: 14 start-page: 255 issue: 1 year: 2020 ident: 1799_CR20 publication-title: Appl. Anal. Discrete Math. doi: 10.2298/AADM190924020W – volume: 23 start-page: 77 issue: 1 year: 2020 ident: 1799_CR33 publication-title: Math. Inequal. Appl. – volume: 13 start-page: 240 year: 2019 ident: 1799_CR36 publication-title: Appl. Anal. Discrete Math. doi: 10.2298/AADM171015001Y – volume: 21 start-page: 413 year: 2021 ident: 1799_CR40 publication-title: Comput. Methods Funct. Theory doi: 10.1007/s40315-020-00352-7 – volume: 23 start-page: 512 issue: 2 year: 1992 ident: 1799_CR5 publication-title: SIAM J. Math. Anal. doi: 10.1137/0523025 – volume: 27 start-page: 823 issue: 3 year: 1996 ident: 1799_CR14 publication-title: SIAM J. Math. Anal. doi: 10.1137/0527044 – ident: 1799_CR42 doi: 10.1007/s13398-020-00992-3 – volume: 508 start-page: 125889, 23 year: 2022 ident: 1799_CR28 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2021.125889 |
| SSID | ssj0052212 |
| Score | 2.3184001 |
| Snippet | Let
K
r
be the complete elliptic integral of the first kind defined on
0
,
1
. By virtue of the auxiliary function
H
f
,
g
=
f
′
/
g
′
g
-
f
, we prove that... Let Kr be the complete elliptic integral of the first kind defined on 0,1. By virtue of the auxiliary function Hf,g=f′/g′g-f, we prove that the function... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 29 |
| SubjectTerms | Convexity Mathematics Mathematics and Statistics |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwEA8yfdAHv8XplDz4poH1wyZ5lOFwqEPUyd7KJU1hMDpZq-zP95J-DEUFpW_tJZS7y92vzeV3hJxd-pwrTyUMQIYsBKOZEACMm1QC98GLtGPXv-PDoRiP5UN1KCyvq93rLUkXqZvDbl3XetVWn1svkgyR4yqmO2EbNjw-vdTxFwFFuccZoiR6V1Adlfl-js_paIkxv2yLumzT3_rfe26TzQpd0qvSHXbIisl2ycZ9Q82a75FRz9aZLxB8U8gSimt6Vlh6XHtjkGGwsn8YKA6gNlSgVQ21dR0YWTQdlNwSUzpLnUR_gtiR3uJn_T4Z9a-fezes6q3ANC66gnElAvB5GkYigijVyhgltRbSgJFSGYsEtdAmAQ8gTFSqfTCGK93lkiPECA5IK5tl5pBQxBCpUl1h0Oz4eRgAXon2Ekx7CAf8qE28WsWxrojHbf-LadxQJjuVxaiy2KksXrTJeTPmtaTd-FW6U1surpZgHgcI5gKBeCtok4vaUsvHP8929DfxY7JuW9CXldwd0irmb-aErOn3YpLPT51rfgDoQ99a priority: 102 providerName: Springer Nature |
| Title | Convexity and Monotonicity Involving the Complete Elliptic Integral of the First Kind |
| URI | https://link.springer.com/article/10.1007/s00025-022-01799-x https://www.proquest.com/docview/3256384393 |
| Volume | 78 |
| WOSCitedRecordID | wos000890291300003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1420-9012 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0052212 issn: 1422-6383 databaseCode: K7- dateStart: 20230201 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central Database Suite (ProQuest) customDbUrl: eissn: 1420-9012 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0052212 issn: 1422-6383 databaseCode: BENPR dateStart: 20230201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1420-9012 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0052212 issn: 1422-6383 databaseCode: M2P dateStart: 20230201 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1420-9012 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0052212 issn: 1422-6383 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwED9080Ef_Banc-TBNw2uHzbJk-hwOObGUCe-lSRNQZBublP253tJ2w0FfZFCH9oklP4ud79LLncAp5c-Y8pTCZVShDSURlPOpaTMpEIyX3qRdtn171m_z19exKBYcJsWYZWlTnSKOhlpu0Z-EaBtDjiaz-Bq_E5t1Si7u1qU0FiFKjIbz4Z09fxBqYmRWuS7nSE6XNg5KA7NuKNzTVfI1cayW5kUdP7dMC3Z5o8NUmd32lv__eJt2CwYJ7nORWQHVky2Cxu9RbrW6R4MWzb2fI6EnMgsITjPRzObMtc-6GSowOyqA8EOxKoPRNoQG-uB2kaTTp5v4o2MUtei_Yp8knTR1d-HYfv2qXVHi3oLVONEnFGmeCB9loYRj2SUamWMElpzYaQRQhnLDjXXJpGelGGiUu1LY5jSTSYY0o7gACrZKDOHQJBXpEo1uUFRQJcxkHgl2kvQFCJF8KMaeOXPjnWRjNzWxHiLF2mUHUAxAhQ7gOJ5Dc4WfcZ5Ko4_W9dLVOJiWk7jJSQ1OC9xXb7-fbSjv0c7hnVbhj6P5q5DZTb5MCewpj9nr9NJA6o3t_3BQwNWu4w2nIji_eHx-QuGxOwp |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3PT9swFH5iMAk4jG1sohtsPmynYdE4IbYP04QKFVV_iAOVegu240iVqrTQAuWf4m_cs5O0GhK99TDllthWEn9-77P9_D2AH6eMcx3olColIxopa6gQSlFuM6k4U0FsvLp-h_d6YjCQVxvwXJ2FcWGVlU30hjodG7dGfhKibw4Fus_wz-SWuqxRbne1SqFRwKJtnx5xyjb93TrH_v3JWPPiunFJy6wC1CDcZpRrESrGsygWsYozo63V0hghrbJSaus4kBHGpipQKkp1ZpiylmtT55Kjcw2x3TewFTllMRcqyK4qy49UpthdjXCChy8blod0_FG9uk8c62Ln3RiQdP6vI1yy2xcbst7PNff-tz_0Ht6VjJqcFUPgA2zY_CPsdhdytNN96DdcbP0cJxxE5SlBOzaeOUlgd6OVo4F2qyoEKxBnHhHJlrhYFrSmhrQKPY0RGWe-RHOIfJm0h3n6Cfpr-a7PsJmPc3sABHlTpnVdWIQ6AiFUeKUmSNHVIwVicQ2CqnMTU4qtu5wfo2QhE-0BkSAgEg-IZF6DX4s6k0JqZGXpwwoFSWl2pskSAjU4rnC0fPx6a19Wt_Ydti-vu52k0-q1v8IOQ6JXRK4fwubs7t4ewVvzMBtO7775AUHgZt34-gudtEp6 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwEA-iIvrgtzidmgfftGz9sEkeZVocm2Ogk72FJE1hMLqxVdmf7yX9mIoKIn1rL6FcLpdfkrvfIXR54xEiXRk7QrDACYRWDqVCOEQnTBBPuKGy7Ppd0uvR4ZD1P2Tx22j38koyz2kwLE1p1pjGSaNKfGvaMqwmEt1YFHMARa4FJpDe7NefXkpfDOAiv-8MQBIszS_SZr7v4_PStMSbX65I7coT7fz_n3fRdoE68W1uJntoRaf7aOuxomydH6BBy8SfLwCUY5HGGOb6JDO0ueZFOwUnZk4eMDTAxoXAaGts4j3A4yjczjknxniSWIloBJgSd2C7f4gG0f1z68Epai44CiZj5hBJfeGRJAhpKMJESa0lU4oyLTRjUhuEqKjSsXCFCGKZKE9oTaRqEkYAevhHaDWdpPoYYcAWiZRNqsEcYNvoC3hi5cawHAJM8MIackt1c1UQkpu6GGNeUSlblXFQGbcq44sauqraTHM6jl-l6-Uo8mJqzrkPIM-ngMP8GrouR235-efeTv4mfoE2-ncR77Z7nVO0aarU58HedbSazV71GVpXb9loPju3FvsO5ObrIg |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Convexity+and+Monotonicity+Involving+the+Complete+Elliptic+Integral+of+the+First+Kind&rft.jtitle=Resultate+der+Mathematik&rft.au=Tian%2C+Jing-Feng&rft.au=Yang%2C+Zhen-Hang&rft.date=2023-02-01&rft.pub=Springer+Nature+B.V&rft.issn=1422-6383&rft.eissn=1420-9012&rft.volume=78&rft.issue=1&rft.spage=29&rft_id=info:doi/10.1007%2Fs00025-022-01799-x |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1422-6383&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1422-6383&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1422-6383&client=summon |