Generalized Fractal Jensen–Mercer and Hermite–Mercer type inequalities via h-convex functions involving Mittag–Leffler kernel
Peng Xu, Saad Ihsan Butt, Saba Yousaf, Adnan Aslam, Tariq Javed Zia
Abstract
In this paper, we present generalized Jensen-Mercer inequality for a generalized h-convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h-convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature.
Topics & Concepts
MathematicsConvex functionType (biology)Fractional calculusDifferentiable functionKernel (algebra)Hermite polynomialsHadamard transformPure mathematicsRegular polygonApplied mathematicsMathematical analysisGeometryBiologyEcologyMathematical Inequalities and ApplicationsMulti-Criteria Decision MakingMathematical functions and polynomials