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

Year 2020, Volume: 24 Issue: 4, 652 - 664, 01.08.2020

Mahir Kadakal

https://doi.org/10.16984/saufenbilder.699212

https://izlik.org/JA67TA74LN

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

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