New inequalities based on harmonic log-convex functions

Abstract

Harmonic convexity is very important new class of non-convex functions, it gained prominence in the Theory of Inequalities and Applications as well as in the rest of Mathematics's branches. The harmonic convexity of a function is the basis for many inequalities in mathematics. Furthermore, harmonic convexity provides an analytic tool to estimate several known definite integrals like b a e x x n dx, b a e x 2 dx, b a sin x x n dx and b a cos xx n dx ∀n ∈ N, where a, b ∈ (0, ∞). In this article, some un-weighted inequalities of Hermite-Hadamard type for harmonic log-convex functions defined on real intervals are given.

Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives

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