Generalized $(H,\phi )$-Convexity and New Hermite-Hadamard Type Inequalities

Year 2025, Volume: 13 Issue: 4, 201 - 208

Mehmet Zeki Sarikaya

https://doi.org/10.36753/mathenot.1778929

Abstract

In this paper, we introduce a novel class of convex functions, called $(H,\phi)$-convex functions, defined via a general parametric mean $\phi$ and a weighting function $H$. This new convexity notion encompasses several well-known classes such as standard convexity, $s$-convexity, $h$-convexity, and $m$-convexity as particular cases. We provide illustrative examples demonstrating that this class is genuinely more general. Furthermore, we derive a new Hermite-Hadamard type inequality tailored to the $(H, \phi)$ -convex framework. Our results extend and unify various existing inequalities in the literature.

Keywords

Convex function , $h$-convex function , $m$-convex function , $s$ -convex function , Hermite-Hadamard inequality

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