New inequalities based on harmonic log-convex functions

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 d x , ∫ b a e x 2 d x , ∫ b a sin x x n d x and ∫ b a cos x x n d x ∀ 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.