Some new inequalities for generalized <i>h</i>‐convex functions involving local fractional integral operators with Mittag‐Leffler kernel
Wenbing Sun
Abstract
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.
Topics & Concepts
MathematicsFractional calculusKernel (algebra)Mittag-Leffler functionPure mathematicsIntegral transformConvex functionHadamard transformApplied mathematicsRegular polygonMathematical analysisGeometryMathematical Inequalities and ApplicationsMathematical functions and polynomials