Some new inequalities for (α,m1,m2 )-GA convex functions

Abstract

In this manuscript, firstly we introduce and study the concept of (α,m_1,m_2 )-Geometric-Arithmetically (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, m_1 and m_2.

Keywords

• (alpha m1 m2)-ga convex function
• hölder and power-mean inequalities
• hölder-i̇şcan inequality
• hermite-hadamard integral inequality
• power-mean inequality