On $\varphi$-convexity

TL;DR

This paper explores generalized convexity concepts called -convexity and -midconvexity, providing characterizations and relationships between these properties for real-valued functions.

Contribution

It introduces and characterizes -convexity and -midconvexity, extending the understanding of approximate convexity properties.

Findings

Characterizations of -convex and -midconvex functions

Relationship established between -midconvexity and -convexity

Theoretical framework for approximate convexity properties

Abstract

In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and $\varphi$-midconvex functions are obtained. Furthermore, the relationship between $\varphi$-midconvexity and $\varphi$-convexity is established.