Some New Fractional Interval-Valued Inequalities for Set-Valued H(α, 1 − α)-Godunova-Levin Mappings with Applications

Abstract

Convex integral inequalities are an area of substantial interest in mathematical analysis because of their applications to a variety of fields such as optimization, probability theory, and functional analysis. This study derives general forms of convex integral inequalities and presents several new results in the context of H(α, 1−α)-Godunova-Levin mappings via AB fractional integral operators, including Jensen's, Pachapatte, Ostrowski, and Hermite-Hadamard. Additionally, we developed a new type of Jensen-type inequality in sequential form as well as a new Ostrowki-type inequality using a Moore-metric Hausdorff distance approach, which is really an innovative approach to such inequality. Our analysis of convex integral inequalities introduces novel bounds and constraints that characterize the behavior of generalized convex functions. We have further developed several remarks to demonstrate the accuracy of our results that lead to several other generalized convex mappings that have never been introduced so far for this type of generalized mapping, as well as several interesting non-trivial examples.