Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized (E, h)-Convexity
Wedad Saleh, Abdelghani Lakhdari, Ohud Almutairi, Adem Kılıçman
Abstract
In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite–Hadamard-type inequality using generalized (E,h)-convexity and obtain two identities pertaining to these operators, and the respective first- and second-order derivatives are given. In terms of applications, we provide some new generalized trapezoid-type inequalities for generalized (E,h)-convex functions. Finally, some special cases are deduced for different values of δ, E, and h.
Topics & Concepts
MathematicsConvexityKernel (algebra)Fractional calculusPure mathematicsHadamard transformMittag-Leffler functionConvex functionType (biology)Hermite polynomialsRegular polygonInequalityApplied mathematicsMathematical analysisGeometryFinancial economicsBiologyEcologyEconomicsMathematical Inequalities and ApplicationsMathematical functions and polynomialsFunctional Equations Stability Results