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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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 44; no. 3; pp. 2364 - 2380
Main Author: Dragomir, Silvestru Sever
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 01.02.2021
Subjects:
Composite functions
Convex analysis
convex functions
Hadamard fractional integral
Hermite‐Hadamard type inequalities
h‐convex functions
Inequalities
Integrals
Riemann‐Liouville fractional integrals
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5893