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Some new inequalities for generalized h ‐convex functions involving local fractional integral operators with Mittag‐Leffler kernel
Author(s) -
Sun Wenbing
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7081
Subject(s) - mathematics , fractional calculus , kernel (algebra) , mittag leffler function , pure mathematics , integral transform , convex function , hadamard transform , regular polygon , mathematical analysis , geometry
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.