Improved Hermite–Hadamard, Fejér, and Jensen-Type Inequalities for Generalized Logarithmic Godunova–Levin Mappings via Erdélyi–Kober Fractional Operators

Abstract

This article introduces a new class of generalized logarithmic Godunova–Levin type interval-valued mappings. Based on this class, we establish several new Hermite–Hadamard inequalities, including their weighted versions, often referred to as Fejér-type inequalities involving symmetric weight functions, as well as discrete Jensen-type inequalities within the framework of Erdélyi–Kober fractional integrals. The proposed approach provides a unified and generalized framework that extends a wide range of existing results in the literature. Since the introduced convexity class is new, the corresponding results are also novel, even in the case of real-valued mappings. To support the theoretical developments, we present nontrivial illustrative examples along with numerical validations for different choices of fractional parameters. Furthermore, several well-known inequalities are recovered as special cases under appropriate selections of parameters, as demonstrated in the remarks.