New perspective on Jensen type inequalities pertaining to local fractional derivatives

Abstract

We examined and analyzed the characteristics of generalized convex functions defined on fractal sets. We then conducted a comprehensive analysis of the properties associated with these generalized convex functions, and these characteristics were utilized in proving two significant inequalities: the extended Jensen's inequality and the generalized Hermite-Hadamard inequality. Through these inequalities, we derived valuable insights into the behavior of these functions and their relationships with other mathematical concepts. Additionally, practical applications that showcase the significance and applicability of these generalized inequalities in various fields are discussed.