Some New Inequalities for (𝜶,𝒎𝟏, 𝒎𝟐)-GA Convex Functions

Abstract

In this manuscript, firstly we introduce and study the concept of (𝜶,𝒎𝟏, 𝒎𝟐)-GeometricArithmetically (GA) convex functions and some algebraic properties of such type functions. Then, we obtain Hermite-Hadamard type integral inequalities for the newly introduced class of functions by using an identity together with Hölder integral inequality, power-mean integral inequality and Hölder-İşcan integral inequality giving a better approach than Hölder integral inequality. Inequalities have been obtained with the help of Gamma function. In addition, results were obtained according to the special cases of (𝜶,𝒎𝟏 and 𝒎𝟐)Keywords: (𝜶,𝒎𝟏, 𝒎𝟐)-GA convex function, Hölder integral inequality, power-mean inequality, Hölder-İşcan inequality, Hermite-Hadamard integral inequality.