X-convexity and Quasi-X-convex Functions with Applications

In this paper, we define [Formula: see text]-convex and quasi-[Formula: see text]-convex functions. This class of real functions is the generalization of a family of convex functions. Additionally, we provide a thorough analysis of the core characteristics of these functions in this paper, along with numerous examples that help to illustrate the ideas. Furthermore, quasi-[Formula: see text]-convex, semistrictly quasi-[Formula: see text]-convex, and strictly quasi-[Formula: see text]-convex functions are used to study and show its applications on optimization problems.