Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions

By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Nonlinear analysis Ročník 72; číslo 9; s. 3594 - 3601
Hlavní autoři:	Chieu, N.H., Yao, J.-C., Yen, N.D.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Ltd 01.05.2010 Elsevier
Témata:	Construction Equivalence Exact sciences and technology Implicit multifunction Lipschitz-like property Mathematical analysis Mathematics Nonlinearity Normal coderivative Regularity Relationship Robinson metric regularity Sciences and techniques of general use Theorems secondary Lipschitz-like property Robinson metric regularity Normal coderivative Relationship Implicit multifunction primary Nonlinear analysis Mathematical model primary 49J53 47H04 secondary 54C60
ISSN:	0362-546X, 1873-5215
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It turns out that the (reasonable) sufficient conditions for having (Rmr) ⇒ (Llp) are quite different from those for the validity of the reverse implication. The implicit function theorem due to Yen and Yao (2009) [2] serves as a tool for our analysis of (Rmr) and (Llp).
AbstractList	By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It turns out that the (reasonable) sufficient conditions for having (Rmr) ⇒ (Llp) are quite different from those for the validity of the reverse implication. The implicit function theorem due to Yen and Yao (2009) [2] serves as a tool for our analysis of (Rmr) and (Llp). By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It turns out that the (reasonable) sufficient conditions for having (Rmr) [implies] (Llp) are quite different from those for the validity of the reverse implication. The implicit function theorem due to Yen and Yao (2009) [2] serves as a tool for our analysis of (Rmr) and (Llp).
Author	Chieu, N.H. Yao, J.-C. Yen, N.D.
Author_xml	– sequence: 1 givenname: N.H. surname: Chieu fullname: Chieu, N.H. email: nghuychieu@vinhuni.edu.vn, nghuychieu@gmail.com organization: Department of Mathematics, Vinh University, Vinh, Nghe An, Viet Nam – sequence: 2 givenname: J.-C. surname: Yao fullname: Yao, J.-C. email: yaojc@math.nsysu.edu.tw, yaojc@mail.math.nsysu.edu.tw organization: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan – sequence: 3 givenname: N.D. surname: Yen fullname: Yen, N.D. email: ndyen@math.ac.vn organization: Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10307, Viet Nam
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22473363$$DView record in Pascal Francis
BookMark	eNp9kEtv1DAURi1UJKaFPctsEKsEPxI7YYcqXtJISBVI7Kw7zk3nDo492E6r8utJOxULJFh9m3O-xTlnZyEGZOyl4I3gQr85NAEayfnQCNlwNTxhG9EbVXdSdGdsw5WWddfq78_Yec4HzrkwSm_Y9RV6KBRD3tMxVzsst4ihuoo7CjmGasaSyFUJrxcPicpdBWGstivr9lR-1Z5-4Grt4YZiquJU0Xz05KhU8-ILTUtwD-_P2dMJfMYXj3vBvn14__XyU7398vHz5btt7VSnS60ltK3o0ew4jHoSPfSyRS7AuMGAGuSoJmwlQm-gc073XHPueCuGqd1x16sL9vr0e0zx54K52JmyQ-8hYFyyNZ0yqpWDWclXjyRkB35KEBxle0w0Q7qzUrZGKa1Wjp84l2LOCac_iOD2Pr092AD2Pr0V0q7pV0X_paxBHiqXBOT_J749ibgmuiFMNjvC4HCkhK7YMdK_5d-Dw6Dh
CODEN	NOANDD
CitedBy_id	crossref_primary_10_1007_s11590_012_0580_7 crossref_primary_10_1155_2014_892641 crossref_primary_10_1155_2014_792364 crossref_primary_10_1016_j_jmaa_2011_03_026 crossref_primary_10_1137_16M1086881 crossref_primary_10_1080_00036811_2010_483432 crossref_primary_10_1007_s11228_011_0183_y crossref_primary_10_1137_140998469 crossref_primary_10_1007_s10957_012_0058_x crossref_primary_10_1007_s11228_020_00557_x crossref_primary_10_1007_s11117_017_0483_z crossref_primary_10_1016_j_na_2010_11_031 crossref_primary_10_1287_moor_2015_0741
Cites_doi	10.1016/j.jmaa.2007.05.001 10.1287/moor.19.3.753 10.1023/A:1022662120550 10.1023/A:1008775413250 10.1016/0362-546X(85)90024-0 10.1016/j.na.2008.04.005 10.1137/S1052623402419236 10.1137/0713043 10.2307/2154544 10.1023/B:SVAN.0000023396.58424.98 10.1287/moor.9.1.87 10.1137/0712056 10.1016/0362-546X(89)90083-7 10.1007/BF01447734 10.1016/j.jmaa.2007.05.041 10.1016/0022-247X(88)90034-0 10.1016/j.na.2008.02.073 10.1007/s10107-003-0452-0 10.11650/twjm/1500405272 10.1007/BF00938588 10.1137/S1052623495284029
ContentType	Journal Article
Copyright	2009 Elsevier Ltd 2015 INIST-CNRS
Copyright_xml	– notice: 2009 Elsevier Ltd – notice: 2015 INIST-CNRS
DBID	AAYXX CITATION IQODW 7SC 7TB 8FD FR3 H8D JQ2 KR7 L7M L~C L~D
DOI	10.1016/j.na.2009.12.039
DatabaseName	CrossRef Pascal-Francis Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Aerospace Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Aerospace Database Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Aerospace Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering Mathematics
EISSN	1873-5215
EndPage	3601
ExternalDocumentID	22473363 10_1016_j_na_2009_12_039 S0362546X09012644
GroupedDBID	--K --M -~X .~1 0R~ 123 1B1 1RT 1~. 1~5 29N 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABLJU ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD ADTZH AEBSH AECPX AEKER AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 GBLVA HMJ HVGLF HZ~ IHE J1W JJJVA KOM M26 M41 MHUIS MO0 MVM N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SST SSW SSZ T5K TN5 WUQ XPP YQT ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ADNMO AEIPS AFJKZ AGQPQ AIIUN ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7TB 8FD FR3 H8D JQ2 KR7 L7M L~C L~D
ID	FETCH-LOGICAL-c356t-62a4418e7b0ad6f18a824e01a7c97a392d3fe42ea87a5cc680600c0419f4b0c83
ISICitedReferencesCount	18
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000276148000005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0362-546X
IngestDate	Sat Sep 27 18:14:42 EDT 2025 Mon Jul 21 09:18:00 EDT 2025 Tue Nov 18 22:23:37 EST 2025 Sat Nov 29 02:57:57 EST 2025 Fri Feb 23 02:29:50 EST 2024
IsPeerReviewed	true
IsScholarly	true
Issue	9
Keywords	secondary Lipschitz-like property Robinson metric regularity Normal coderivative Relationship Implicit multifunction primary Nonlinear analysis Mathematical model primary 49J53 47H04 secondary 54C60
Language	English
License	https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c356t-62a4418e7b0ad6f18a824e01a7c97a392d3fe42ea87a5cc680600c0419f4b0c83
Notes	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
PQID	753734297
PQPubID	23500
PageCount	8
ParticipantIDs	proquest_miscellaneous_753734297 pascalfrancis_primary_22473363 crossref_primary_10_1016_j_na_2009_12_039 crossref_citationtrail_10_1016_j_na_2009_12_039 elsevier_sciencedirect_doi_10_1016_j_na_2009_12_039
PublicationCentury	2000
PublicationDate	2010-05-01
PublicationDateYYYYMMDD	2010-05-01
PublicationDate_xml	– month: 05 year: 2010 text: 2010-05-01 day: 01
PublicationDecade	2010
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Nonlinear analysis
PublicationYear	2010
Publisher	Elsevier Ltd Elsevier
Publisher_xml	– name: Elsevier Ltd – name: Elsevier
References	Ngai, Théra (b10) 2004; 12 Aubin (b20) 1984; 9 Aragón Artacho, Mordukhovich (b17) 2009 Mordukhovich (b18) 2006 Robinson (b3) 1976; 13 Dontchev, Hager (b21) 1994; 19 Rockafellar (b22) 1985; 9 Lee, Tam, Yen (b9) 2008; 338 Dien, Yen (b11) 1991; 24 Robinson (b16) 1975; 12 Dontchev, Rockafellar (b19) 1996; 6 Borwein (b4) 1986; 48 Ledyaev, Zhu (b8) 1999; 7 Rockafellar, Wets (b30) 1998 Mordukhovich (b29) 2008; 69 Borwein, Zhu (b5) 2005 Yao, Yen (b14) 2009; 34 Mordukhovich (b25) 1993; 340 Borwein, Zhuang (b23) 1988; 134 Yen (b12) 1987; 12 Yen, Yao, Kien (b26) 2008; 338 Yao, Yen (b15) 2009; 5 Levy, Mordukhovich (b27) 2004; 99 Mordukhovich (b28) 1980; 254 Dontchev, Quicampoix, Zlateva (b6) 2006; 13 Jeyakumar, Yen (b1) 2004; 14 Huy, Yao (b7) 2009; 13 Yen, Yao (b2) 2009; 70 Yen (b13) 1997; 93 Penot (b24) 1989; 13 Robinson (10.1016/j.na.2009.12.039_b3) 1976; 13 Yen (10.1016/j.na.2009.12.039_b2) 2009; 70 Yen (10.1016/j.na.2009.12.039_b12) 1987; 12 Aragón Artacho (10.1016/j.na.2009.12.039_b17) 2009 Yen (10.1016/j.na.2009.12.039_b26) 2008; 338 Rockafellar (10.1016/j.na.2009.12.039_b22) 1985; 9 Borwein (10.1016/j.na.2009.12.039_b4) 1986; 48 Ngai (10.1016/j.na.2009.12.039_b10) 2004; 12 Lee (10.1016/j.na.2009.12.039_b9) 2008; 338 Mordukhovich (10.1016/j.na.2009.12.039_b29) 2008; 69 Borwein (10.1016/j.na.2009.12.039_b5) 2005 Ledyaev (10.1016/j.na.2009.12.039_b8) 1999; 7 Mordukhovich (10.1016/j.na.2009.12.039_b28) 1980; 254 Aubin (10.1016/j.na.2009.12.039_b20) 1984; 9 Yao (10.1016/j.na.2009.12.039_b15) 2009; 5 Levy (10.1016/j.na.2009.12.039_b27) 2004; 99 Rockafellar (10.1016/j.na.2009.12.039_b30) 1998 Mordukhovich (10.1016/j.na.2009.12.039_b25) 1993; 340 Jeyakumar (10.1016/j.na.2009.12.039_b1) 2004; 14 Huy (10.1016/j.na.2009.12.039_b7) 2009; 13 Borwein (10.1016/j.na.2009.12.039_b23) 1988; 134 Dontchev (10.1016/j.na.2009.12.039_b21) 1994; 19 Dontchev (10.1016/j.na.2009.12.039_b6) 2006; 13 Dien (10.1016/j.na.2009.12.039_b11) 1991; 24 Penot (10.1016/j.na.2009.12.039_b24) 1989; 13 Robinson (10.1016/j.na.2009.12.039_b16) 1975; 12 Yao (10.1016/j.na.2009.12.039_b14) 2009; 34 Dontchev (10.1016/j.na.2009.12.039_b19) 1996; 6 Mordukhovich (10.1016/j.na.2009.12.039_b18) 2006 Yen (10.1016/j.na.2009.12.039_b13) 1997; 93
References_xml	– volume: 5 start-page: 493 year: 2009 end-page: 506 ident: b15 article-title: Coderivative calculation related to a parametric affine variational inequality. Part 2: Applications publication-title: Pacific J. Optim. – volume: 70 start-page: 2806 year: 2009 end-page: 2815 ident: b2 article-title: Point-based sufficient conditions for metric regularity of implicit multifunctions publication-title: Nonlinear Anal. – volume: 69 start-page: 918 year: 2008 end-page: 924 ident: b29 article-title: Failure of metric regularity for major classes of variational systems publication-title: Nonlinear Anal. – year: 2006 ident: b18 article-title: Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications – volume: 6 start-page: 1087 year: 1996 end-page: 1105 ident: b19 article-title: Characterizations of strong regularity for variational inequalities over polyhedral convex sets publication-title: SIAM J. Optim. – volume: 12 start-page: 195 year: 2004 end-page: 223 ident: b10 article-title: Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization publication-title: Set-Valued Anal. – volume: 24 start-page: 35 year: 1991 end-page: 54 ident: b11 article-title: On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints publication-title: Appl. Math. Optim. – year: 1998 ident: b30 article-title: Variational Analysis – volume: 254 start-page: 1072 year: 1980 end-page: 1076 ident: b28 article-title: Metric approximations and necessary conditions for optimality for general classes of nonsmooth extremal problems publication-title: Dokl. Akad. Nauk SSSR – volume: 34 start-page: 157 year: 2009 end-page: 172 ident: b14 article-title: Coderivative calculation related to a parametric affine variational inequality. Part 1: Basic calculations publication-title: Acta Math. Vietnam. – volume: 338 start-page: 467 year: 2008 end-page: 478 ident: b26 article-title: Covering poperties at positive-order rates of multifuctions and some related topics publication-title: J. Math. Anal. Appl. – volume: 340 start-page: 1 year: 1993 end-page: 35 ident: b25 article-title: Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions publication-title: Trans. Amer. Math. Soc. – volume: 134 start-page: 441 year: 1988 end-page: 459 ident: b23 article-title: Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps publication-title: J. Math. Anal. Appl. – volume: 338 start-page: 11 year: 2008 end-page: 22 ident: b9 article-title: Normal coderivative for multifunctions and implicit function theorems publication-title: J. Math. Anal. Appl. – volume: 9 start-page: 867 year: 1985 end-page: 885 ident: b22 article-title: Lipschitzian properties of multifunctions publication-title: Nonlinear Anal. – volume: 13 start-page: 497 year: 1976 end-page: 513 ident: b3 article-title: Stability theory for systems of inequalities, II. Differentiable nonlinear systems publication-title: SIAM J. Numer. Anal. – volume: 48 start-page: 9 year: 1986 end-page: 52 ident: b4 article-title: Stability and regular points of inequality systems publication-title: J. Optim. Theory Appl. – volume: 12 start-page: 754 year: 1975 end-page: 769 ident: b16 article-title: Stability theory for systems of inequalities, I. Linear systems publication-title: SIAM J. Numer. Anal. – volume: 13 start-page: 281 year: 2006 end-page: 297 ident: b6 article-title: Aubin criterion for metric regularity publication-title: J. Convex Anal. – volume: 7 start-page: 209 year: 1999 end-page: 238 ident: b8 article-title: Implicit multifunctions theorems publication-title: Set-Valued Anal. – year: 2005 ident: b5 article-title: Techniques of Variational Analysis – year: 2009 ident: b17 article-title: Metric regularity and Lipschitzian stability of parametric variational systems publication-title: Nonlinear Anal. – volume: 19 start-page: 753 year: 1994 end-page: 768 ident: b21 article-title: Implicit functions, Lipschitz maps, and stability in optimization publication-title: Math. Oper. Res. – volume: 12 start-page: 17 year: 1987 end-page: 28 ident: b12 article-title: Implicit function theorems for set-valued maps publication-title: Acta Math. Vietnam. – volume: 13 start-page: 629 year: 1989 end-page: 643 ident: b24 article-title: Metric regularity, openness and Lipschitzian behavior of multifunctions publication-title: Nonlinear Anal. TMA – volume: 14 start-page: 1106 year: 2004 end-page: 1127 ident: b1 article-title: Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization publication-title: SIAM J. Optim. – volume: 93 start-page: 199 year: 1997 end-page: 225 ident: b13 article-title: Stability of the solution set of perturbed nonsmooth inequality systems and application publication-title: J. Optim. Theory Appl. – volume: 9 start-page: 87 year: 1984 end-page: 111 ident: b20 article-title: Lipschitz behavior of solutions to convex minimization problems publication-title: Math. Oper. Res. – volume: 99 start-page: 311 year: 2004 end-page: 327 ident: b27 article-title: Coderivatives in parametric optimization publication-title: Math. Program. – volume: 13 start-page: 47 year: 2009 end-page: 65 ident: b7 article-title: Stability of implicit multifunctions in Asplund spaces publication-title: Taiwanese J. Math. – volume: 13 start-page: 281 year: 2006 ident: 10.1016/j.na.2009.12.039_b6 article-title: Aubin criterion for metric regularity publication-title: J. Convex Anal. – volume: 338 start-page: 11 year: 2008 ident: 10.1016/j.na.2009.12.039_b9 article-title: Normal coderivative for multifunctions and implicit function theorems publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.05.001 – year: 2009 ident: 10.1016/j.na.2009.12.039_b17 article-title: Metric regularity and Lipschitzian stability of parametric variational systems publication-title: Nonlinear Anal. – volume: 19 start-page: 753 year: 1994 ident: 10.1016/j.na.2009.12.039_b21 article-title: Implicit functions, Lipschitz maps, and stability in optimization publication-title: Math. Oper. Res. doi: 10.1287/moor.19.3.753 – volume: 93 start-page: 199 year: 1997 ident: 10.1016/j.na.2009.12.039_b13 article-title: Stability of the solution set of perturbed nonsmooth inequality systems and application publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1022662120550 – volume: 7 start-page: 209 year: 1999 ident: 10.1016/j.na.2009.12.039_b8 article-title: Implicit multifunctions theorems publication-title: Set-Valued Anal. doi: 10.1023/A:1008775413250 – volume: 9 start-page: 867 year: 1985 ident: 10.1016/j.na.2009.12.039_b22 article-title: Lipschitzian properties of multifunctions publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(85)90024-0 – volume: 70 start-page: 2806 year: 2009 ident: 10.1016/j.na.2009.12.039_b2 article-title: Point-based sufficient conditions for metric regularity of implicit multifunctions publication-title: Nonlinear Anal. doi: 10.1016/j.na.2008.04.005 – year: 1998 ident: 10.1016/j.na.2009.12.039_b30 – volume: 14 start-page: 1106 year: 2004 ident: 10.1016/j.na.2009.12.039_b1 article-title: Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623402419236 – volume: 13 start-page: 497 year: 1976 ident: 10.1016/j.na.2009.12.039_b3 article-title: Stability theory for systems of inequalities, II. Differentiable nonlinear systems publication-title: SIAM J. Numer. Anal. doi: 10.1137/0713043 – volume: 12 start-page: 17 issue: 2 year: 1987 ident: 10.1016/j.na.2009.12.039_b12 article-title: Implicit function theorems for set-valued maps publication-title: Acta Math. Vietnam. – volume: 340 start-page: 1 year: 1993 ident: 10.1016/j.na.2009.12.039_b25 article-title: Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions publication-title: Trans. Amer. Math. Soc. doi: 10.2307/2154544 – volume: 12 start-page: 195 year: 2004 ident: 10.1016/j.na.2009.12.039_b10 article-title: Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization publication-title: Set-Valued Anal. doi: 10.1023/B:SVAN.0000023396.58424.98 – volume: 9 start-page: 87 year: 1984 ident: 10.1016/j.na.2009.12.039_b20 article-title: Lipschitz behavior of solutions to convex minimization problems publication-title: Math. Oper. Res. doi: 10.1287/moor.9.1.87 – volume: 12 start-page: 754 year: 1975 ident: 10.1016/j.na.2009.12.039_b16 article-title: Stability theory for systems of inequalities, I. Linear systems publication-title: SIAM J. Numer. Anal. doi: 10.1137/0712056 – volume: 13 start-page: 629 year: 1989 ident: 10.1016/j.na.2009.12.039_b24 article-title: Metric regularity, openness and Lipschitzian behavior of multifunctions publication-title: Nonlinear Anal. TMA doi: 10.1016/0362-546X(89)90083-7 – volume: 254 start-page: 1072 year: 1980 ident: 10.1016/j.na.2009.12.039_b28 article-title: Metric approximations and necessary conditions for optimality for general classes of nonsmooth extremal problems publication-title: Dokl. Akad. Nauk SSSR – volume: 24 start-page: 35 year: 1991 ident: 10.1016/j.na.2009.12.039_b11 article-title: On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints publication-title: Appl. Math. Optim. doi: 10.1007/BF01447734 – volume: 34 start-page: 157 year: 2009 ident: 10.1016/j.na.2009.12.039_b14 article-title: Coderivative calculation related to a parametric affine variational inequality. Part 1: Basic calculations publication-title: Acta Math. Vietnam. – volume: 338 start-page: 467 year: 2008 ident: 10.1016/j.na.2009.12.039_b26 article-title: Covering poperties at positive-order rates of multifuctions and some related topics publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.05.041 – volume: 134 start-page: 441 year: 1988 ident: 10.1016/j.na.2009.12.039_b23 article-title: Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(88)90034-0 – volume: 69 start-page: 918 year: 2008 ident: 10.1016/j.na.2009.12.039_b29 article-title: Failure of metric regularity for major classes of variational systems publication-title: Nonlinear Anal. doi: 10.1016/j.na.2008.02.073 – year: 2005 ident: 10.1016/j.na.2009.12.039_b5 – year: 2006 ident: 10.1016/j.na.2009.12.039_b18 – volume: 99 start-page: 311 year: 2004 ident: 10.1016/j.na.2009.12.039_b27 article-title: Coderivatives in parametric optimization publication-title: Math. Program. doi: 10.1007/s10107-003-0452-0 – volume: 13 start-page: 47 year: 2009 ident: 10.1016/j.na.2009.12.039_b7 article-title: Stability of implicit multifunctions in Asplund spaces publication-title: Taiwanese J. Math. doi: 10.11650/twjm/1500405272 – volume: 5 start-page: 493 year: 2009 ident: 10.1016/j.na.2009.12.039_b15 article-title: Coderivative calculation related to a parametric affine variational inequality. Part 2: Applications publication-title: Pacific J. Optim. – volume: 48 start-page: 9 year: 1986 ident: 10.1016/j.na.2009.12.039_b4 article-title: Stability and regular points of inequality systems publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00938588 – volume: 6 start-page: 1087 year: 1996 ident: 10.1016/j.na.2009.12.039_b19 article-title: Characterizations of strong regularity for variational inequalities over polyhedral convex sets publication-title: SIAM J. Optim. doi: 10.1137/S1052623495284029
SSID	ssj0001736
Score	2.020758
Snippet	By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property... By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp)...
SourceID	proquest pascalfrancis crossref elsevier
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	3594
SubjectTerms	Construction Equivalence Exact sciences and technology Implicit multifunction Lipschitz-like property Mathematical analysis Mathematics Nonlinearity Normal coderivative Regularity Relationship Robinson metric regularity Sciences and techniques of general use Theorems
Title	Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions
URI	https://dx.doi.org/10.1016/j.na.2009.12.039 https://www.proquest.com/docview/753734297
Volume	72
WOSCitedRecordID	wos000276148000005&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5215 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001736 issn: 0362-546X databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLbKxgMIcRkgymXyAy88pDixEzuP0xgaaFRIDNS3yHGdkVGlVdNOE-LHcxzbuTAxARIvURslddTz5fizzznfQeglzLEhSaUJ_UcyYCxmQUpJHsSME66igrGmvuLLCZ9OxWyWfhyNfvhamIsFrypxeZmu_qup4RwY25TO_oW52x-FE_AZjA5HMDsc_8jwbXrb13JVt3lYvs7LtIxeN7LNpge96VzXhA9O4FoTUfgeLMpvui3ebwQlmpzzcmNzD8082O3xOVY7tXob0uRjWo2TLmug1Ftb0XU8aT2MtOGeSXDYndOu8OvNpL8RYWPovY2ItkKmS0fyVVkxa7oVwnxjnazgFBbAtozTe2Ee9dCW9lwqjW0XZDc908SOecX1212I80klrQqp2eS1Okm_CGp_Ms9kHokAFzJ88AbajXicglvfPXh3NHvfzuQhp4mXHzM3uDC3zQ8cjvM7WnNnJWt42QrbJeXKhN-wmNP76K5bfuADC5sHaKSrPXTPLUWwc_T1Hrrd06mEbx9acd_6ITobIAw7hGGPMGwRhjuEYUAYHiIMe4ThZYE9wvAQYY_Q57dHp4fHgevXESgaJ5sgiSSQa6F5TuQ8KUIhRcQ0CSVXKZdAxOe00CzSUnAZK5UIAmxbERamBcuJEvQx2qmWlX6CMNWEyjzhRKc5C1UuwYEIZbhyMc-VSMbotf-7M-XE7E1PlUXmsxbPs0qaHqtpFkYZGGiMXrV3rKyQyzXXUm_BzBFRSzAzANs1d-0PjN0OAyzZiI7SMcLe-hk4cROZk5VebuuMx5RTYIb86T-N_Azd6l7I52hns97qF-imutiU9Xrfofonxt_CeQ
linkProvider	Elsevier
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=Relationships+between+Robinson+metric+regularity+and+Lipschitz-like+behavior+of+implicit+multifunctions&rft.jtitle=Nonlinear+analysis&rft.au=Chieu%2C+N.H.&rft.au=Yao%2C+J.-C.&rft.au=Yen%2C+N.D.&rft.date=2010-05-01&rft.pub=Elsevier+Ltd&rft.issn=0362-546X&rft.eissn=1873-5215&rft.volume=72&rft.issue=9&rft.spage=3594&rft.epage=3601&rft_id=info:doi/10.1016%2Fj.na.2009.12.039&rft.externalDocID=S0362546X09012644
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0362-546X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0362-546X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0362-546X&client=summon