$X$-convexity and Applications of Quasi-$X$-Convex Functions
Musavvir Ali, Ehtesham Akhter

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 -convex, strictly -convex, quasi--convex, strictly quasi--convex, and semi-strictly quasi--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--convex, semistrictly quasi--convex, and strictly quasi--convex functions.
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Taxonomy
TopicsOptimization and Variational Analysis · Nuclear Receptors and Signaling
