$X$-convexity and Applications of Quasi-$X$-Convex Functions

TL;DR

This paper introduces a new class of functions called quasi-$X$-convex functions, generalizing convex functions, and explores their properties and applications in optimization problems.

Contribution

It defines and studies the properties of quasi-$X$-convex and related functions, extending convex analysis and applying it to optimization.

Findings

Defined quasi-$X$-convex functions and their variants.

Analyzed fundamental properties with examples.

Applied to optimization problems.

Abstract

A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly quasi-$X$-convex functions. Moreover, in this paper, we give a detailed study of the fundamental properties of these functions with various examples, supporting the concepts. Finally, the study of optimization problems employs quasi-$X$-convex, semistrictly quasi-$X$-convex, and strictly quasi-$X$-convex functions.