Hermite‐Hadamard type inequalities for generalized Riemann‐Liouville fractional integrals of h‐convex functions
In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals Ia+,gαf and Ib−,gαf, where g is a strictly increasing function on a,b, having a continuous derivative on a,b and under the assumption that the composite function f∘g−1 is h...
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| Vydáno v: | Mathematical methods in the applied sciences Ročník 44; číslo 3; s. 2364 - 2380 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Freiburg
Wiley Subscription Services, Inc
01.02.2021
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| ISSN: | 0170-4214, 1099-1476 |
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| Abstract | In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals
Ia+,gαf and
Ib−,gαf, where g is a strictly increasing function on
a,b, having a continuous derivative on
a,b and under the assumption that the composite function f∘g−1 is h ‐convex on
ga,gb. Some applications for Hadamard fractional integrals and s‐Godunova‐Levin type convex functions are also provided. |
|---|---|
| AbstractList | In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals
Ia+,gαf and
Ib−,gαf, where g is a strictly increasing function on
a,b, having a continuous derivative on
a,b and under the assumption that the composite function f∘g−1 is h ‐convex on
ga,gb. Some applications for Hadamard fractional integrals and s‐Godunova‐Levin type convex functions are also provided. In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals and , where g is a strictly increasing function on having a continuous derivative on and under the assumption that the composite function f ∘ g −1 is h ‐convex on . Some applications for Hadamard fractional integrals and s ‐Godunova‐Levin type convex functions are also provided. In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals Ia+,gαf and Ib−,gαf, where g is a strictly increasing function ona,b, having a continuous derivative on a,b and under the assumption that the composite function f∘g−1 is h ‐convex on ga,gb. Some applications for Hadamard fractional integrals and s‐Godunova‐Levin type convex functions are also provided. |
| Author | Dragomir, Silvestru Sever |
| Author_xml | – sequence: 1 givenname: Silvestru Sever orcidid: 0000-0003-2902-6805 surname: Dragomir fullname: Dragomir, Silvestru Sever email: sever.dragomir@vu.edu.au organization: University of the Witwatersrand |
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| Cites_doi | 10.7153/jmi-10-74 10.1186/1029-242X-2013-220 10.1186/1029-242X-2013-364 10.1016/j.camwa.2009.07.073 10.1186/1029-242X-2013-326 10.15352/afa/1399900993 10.1186/s13660-017-1318-y 10.3906/mat-1411-61 10.1016/j.jmaa.2006.02.086 |
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| References | 2017; 20 2009; 58 2010; 1 2007; 326 2010; 79 2017; 2017 1978; 23 2000 2017; 14 2013; 2013 1995; 21 2016; 10 1985 2006 2016; 40 2010; 4 Kilbas A (e_1_2_6_4_1) 2006 e_1_2_6_20_1 Latif MA (e_1_2_6_15_1) 2010; 4 e_1_2_6_9_1 e_1_2_6_8_1 Godunova EK (e_1_2_6_18_1) 1985 e_1_2_6_5_1 e_1_2_6_7_1 e_1_2_6_6_1 e_1_2_6_13_1 e_1_2_6_14_1 Dragomir SS (e_1_2_6_3_1) 2017; 14 Sarikaya MZ (e_1_2_6_16_1) 2010; 79 Dragomir SS (e_1_2_6_19_1) 1995; 21 e_1_2_6_2_1 Dragomir SS (e_1_2_6_10_1) 2017; 20 Dragomir SS (e_1_2_6_12_1) 2017; 20 e_1_2_6_17_1 Breckner WW (e_1_2_6_21_1) 1978; 23 Dragomir SS (e_1_2_6_11_1) 2017; 20 |
| References_xml | – volume: 2013 start-page: 364 year: 2013 article-title: Fractional Hermite‐Hadamard inequalities for ( ; )‐logarithmically convex functions publication-title: J Inequal Appl – volume: 10 start-page: 901 issue: 4 year: 2016 end-page: 918 article-title: Symmetrized convexityandinequalities Hermite‐Hadamard type publication-title: J Math Inequal – volume: 2013 start-page: 326 year: 2013 article-title: Ostrowski‐type inequalities via ‐convex functions with applications to special publication-title: J Inequal Appl – start-page: 138 year: 1985 end-page: 142 – volume: 20 start-page: Art. 40 year: 2017 article-title: Some inequalities of Hermite‐Hadamard type for convex functions and Riemann‐Liouville fractional integrals publication-title: RGMIA Res Rep Coll – volume: 58 start-page: 1869 issue: 9 year: 2009 end-page: 1877 article-title: Properties of ‐convex functions related to the Hermite‐Hadamard‐Fejér inequalities publication-title: Comput Math Appl – volume: 23 start-page: 13 issue: 37 year: 1978 end-page: 20 article-title: Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen räumen publication-title: (German) Publ Inst Math (Beograd) (NS) – volume: 2017 start-page: 55 year: 2017 article-title: Certain Hermite‐Hadamard type inequalities via generalized ‐fractional integrals publication-title: Journal of Inequalities and Applications – year: 2006 – volume: 4 start-page: 1473 issue: 29‐32 year: 2010 end-page: 1482 article-title: On some inequalities for ‐convex functions publication-title: Int J Math Anal (Ruse) – year: 2000 – volume: 14 start-page: Article 1, pp. 1 issue: 1 year: 2017 end-page: 287 article-title: Ostrowski type inequalities for Lebesgue integral: a survey of recent results publication-title: Australian J Math Anal Appl – volume: 40 start-page: 471 year: 2016 end-page: 486 article-title: New inequalities for fractional integrals and their applications publication-title: Turk J Math – volume: 326 start-page: 303 issue: 1 year: 2007 end-page: 311 article-title: On ‐convexity publication-title: J Math Anal Appl – volume: 20 start-page: Art. 76 year: 2017 article-title: Hermite‐Hadamard type inequalities of first kind for generalized Riemann‐Liouville fractional integrals publication-title: RGMIA Res Rep Coll – volume: 21 start-page: 335 issue: 3 year: 1995 end-page: 341 article-title: Some inequalities of Hadamard type publication-title: Soochow J Math – volume: 1 start-page: 51 issue: 1 year: 2010 end-page: 58 article-title: On Minkowski and Hermite‐Hadamard integral inequalities via fractional integration publication-title: Ann Funct Anal – volume: 2013 start-page: 220 year: 2013 article-title: On some new Hermite‐Hadamard inequalities involving Riemann‐Liouville fractional integrals publication-title: J Inequal Appl – volume: 20 start-page: Art. 79 year: 2017 article-title: Hermite‐Hadamard type inequalities of second kind for generalized Riemann‐Liouville fractional integrals publication-title: RGMIA Res. 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| Snippet | In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals
Ia+,gαf and
Ib−,gαf, where g is... In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals and , where g is a strictly... In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals Ia+,gαf and Ib−,gαf, where g is... |
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| SubjectTerms | Composite functions Convex analysis convex functions Hadamard fractional integral Hermite‐Hadamard type inequalities h‐convex functions Inequalities Integrals Riemann‐Liouville fractional integrals |
| Title | Hermite‐Hadamard type inequalities for generalized Riemann‐Liouville fractional integrals of h‐convex functions |
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