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Journal of Convex Analysis 29 (2022), No. 1, 205--220
Copyright Heldermann Verlag 2022

Some Integral Inequalities for Arithmetically and Geometrically Convex Functions of Two Variables

Vahid Darvish
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China

Tahere A. Roushan
Dept. of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Svetlin G. Georgiev
Sorbonne University, Paris, France

Sever S. Dragomir
Dept. of Mathematics, School of Engineering and Science,, Victoria University, Melbourne, Australia

We introduce arithmetic-geometrically and geometric-geometrically convex functions for two variables. Then, we prove Hermite-Hadamard type inequalities for these functions. As applications, some new inequalities for unitarily invariant norms are established.

Keywords: Hermite-Hadamard inequality, convex function, arithmetic-geometrically convex, unitarily invariant norm.

MSC: 47A63, 15A60, 47B05, 47B10, 26D15.

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