Integral inequalities via generalized convex functions

Abstract

In this paper, we introduce and investigate a new class of generalized convex functions, called generalized log-convex function. We establish some new Hermite-Hadamard integral inequalities via generalized log-convex functions. Our results represent refinement and improvement of the previously known results. Several special cases are also discussed. Geometric mean:G3. Logarithmic mean: Quadratic mean:K(a, b) = a 2 + b 2 2 , ∀a, b ∈ R + .