Quantum symmetric analysis of interval-valued mappings based on generalized Hukuhara differences

Abstract

The primary aim of this investigation is to examine the quantum symmetric differentiability and anti-derivative charac-teristics of interval-valued (I.V.) mappings utilizing generalized Hukuhara differences. Initially, we present the concepts of the I.V. left quantum symmetric derivative operator and offer its characterization. We present the left quantum symmetric integral operator and its essential properties, grounded in the newly proposed derivative operator. Subsequently, we examine their various essential properties. Finally, we present the applications of our proposed operators to integral inequalities concerning I.V. convex mappings and totally ordered convex mappings. Moreover, the validity of our results is corroborated by numerical and graphical representations