- Mathematical Sciences and Applications E-Notes
- Vol: 10 Issue: 2
- $\left(m_{1},m_{2}\right) $-Geometric Arithmetically Convex Functions and Related Inequalities
$\left(m_{1},m_{2}\right) $-Geometric Arithmetically Convex Functions and Related Inequalities
Authors : Mahir Kadakal
Pages : 63-71
View : 8 | Download : 2
Publication Date : 2022-06-01
Article Type : Research
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