Comparative Analysis of Preinvexity, Pseudo-Convexity, and Quasi-Convexity on Fractal Sets

Abstract

This paper extends the study of generalized convexity on fractal sets by exploring preinvexity, pseudo-convexity, and quasi-convexity within the framework of local fractional integrals. While prior research has primarily focused on \((\tilde{h}_1, \tilde{h}_2)\)-preinvex mappings, we establish novel relationships between these generalized convexities and derive new integral inequalities that bridge their theoretical frameworks. Furthermore, we provide a comparative analysis of their properties and applications in numerical integration. To illustrate the relevance of our results, we include concrete examples and discuss potential interdisciplinary applications in fields such as fluid dynamics and fractal growth. The findings significantly enhance the understanding of generalized convexity on fractal sets, offering a broader theoretical and practical perspective.