Some New Inequalities Involving Generalized Convex Functions in the Katugampola Fractional Setting (Contemporary Mathematics, 2025)
In this study, we explore a new class of convex functions termed cr-log-h-convex functions within the framework of interval-valued functions and the cr-order. We introduce and analyze fundamental properties of these functions and establish several Hermite-Hadamard inequalities by employing Katugampola fractional integrals. To illustrate the theoretical results, we present numerical examples that validate the proposed inequalities. This work extends the understanding of convexity concepts and their applications, offering a broader perspective on inequalities in real analysis and fuzzy systems.
Keywords: integral inequalities; generalized convex functions; Katugampola fractional operators; Hermite-Hadamard inequality; symmetric function