Novel Fuzzy Versions of Generalized Fractional Integrals and Related Mathematical Inequalities via Newly Defined Fuzzy Convexity (Contemporary Mathematics, 2025)
In this study, the main aim is to establish a set of novel inequalities that enhance the mathematical inequalities discussed. This paper introduces a new fuzzy fractional integral framework along with associated inequalities by defining a novel class of fuzzy-valued convex mappings, termed up and down (U ·D) fuzzy-valued generalized strong ƛ-convex mappings. Some new and classical exceptional cases are also obtained for generalized fuzzy fractional integral operators and U ·D-fuzzy-valued generalized strong A convex mapping. Some new forms of Hermite-Hadamard inequalities are also derived through fuzzy generalized fractional integrals and extends Pachpatte-type inequalities by applying products of U ·D-fuzzy-valued generalized strong ƛ-convex mappings. Additionally, several midpoint inequalities are introduced. Some open problems are also presented for future discussion.
Keywords: Up and down generalized strong ƛ-convex mapping; fuzzy generalized fractional integrals; Hermite-Hadamard inequalities; Pachpatte-type inequalities; Convex analysis