Some new inequalities for generalized h‐convex functions involving local fractional integral operators with Mittag‐Leffler kernel

In this paper, we firstly construct two local fractional integral operators with Mittag‐Leffler kernel on Yang's fractal sets. Then, two local fractional integral identities with the first‐ and second‐order derivatives are derived. With these as auxiliary tools, we establish some new Hermite‐Ha...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 44; no. 6; pp. 4985 - 4998
Main Author: Sun, Wenbing
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 01.04.2021
Subjects:
Convex analysis
Fractional calculus
generalized h‐convex function
Hermite‐Hadamard–type inequalities
Identities
Inequalities
Integrals
Kernels
local fractional integrals operators
Mittag‐Leffler kernel
Operators (mathematics)
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:In this paper, we firstly construct two local fractional integral operators with Mittag‐Leffler kernel on Yang's fractal sets. Then, two local fractional integral identities with the first‐ and second‐order derivatives are derived. With these as auxiliary tools, we establish some new Hermite‐Hadamard–type local fractional integral inequalities involving the local fractional integral operators with Mittag‐Leffler kernel for generalized h‐convex functions. In addition, we obtain some special inequalities when the parameter β and function h take special values. Finally, two examples are given to illustrate the application of the results.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7081