$\left(m_{1},m_{2}\right) $-Geometric Arithmetically Convex Functions and Related Inequalities

Year 2022, Volume: 10 Issue: 2, 63 - 71, 01.06.2022

Mahir Kadakal

Abstract

In this manuscript, we introduce and study the concept of $\left( m_{1},m_{2}\right) $-geometric arithmetically (GA) convex functions and their some algebric properties. In addition, we obtain Hermite-Hadamard type inequalities for the newly introduced this type of functions whose derivatives in absolute value are the class of $\left( m_{1},m_{2}\right) $ -GA-convex functions by using both well-known power mean and Hölder's integral inequalities.

Keywords

Convex function, m-convex function, (m1;m2)-GA convex function, Hermite-Hadamard inequality

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