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Journal of Convex Analysis 29 (2022), No. 1, 257--268
Copyright Heldermann Verlag 2022

On (h,g;m)-Convexity and the Hermite-Hadamard Inequality

Maja Andric
Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

Josip Pecaric
People's Friendship University, 117198 Moscow, Russia

A new class of (h,g;m)-convex functions is presented, together with its properties, thus generalizing several varieties of convexity such as (h-m)-convex functions, (s,m)-Godunova-Levin functions or exponentially (s,m)-convex functions. Also, the Hermite-Hadamard inequality for an (h,g;m)-convex function is proved and some special results are pointed out.

Keywords: Convex function, Hermite-Hadamard inequality.

MSC: 26A51, 26D15.

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