X-Convexity and Quasi-X-Convex Functions with Applications.

In this paper, we define X-convex and quasi-X-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-X-convex, semistrictly quasi-X-convex, and strictly quasi-X-convex functions are used to study and show its applications on optimization problems. [ABSTRACT FROM AUTHOR]

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