New perspective on Jensen type inequalities pertaining to local fractional derivatives

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 con-vex 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 mathemat-ical concepts. Additionally, practical applications that showcase the significance and applicability of these generalized inequalities in various fields are discussed.