(k, g)-Fractional Integral Hermite-Hadamard Type Inequalities Involving Convex and Symmetric Functions

Abstract

This paper examines the importance of generalised (k, g) fractional integral operators within the framework of mathematical inequalities. We introduce innovative generalised fractional integral Hermite-Hadamard inequalities, which, to our knowledge, constitute a new advancement in the area. These inequalities are formulated using contemporary generalised fractional integral operators and underscore the complex interconnections among convexity, symmetry, and fractional calculus. align, we present fractional integral Hermite-Hadamard-type inequalities that utilise these generalised operators, offering an expanded framework for comprehending the characteristics of convex and symmetric functions. Our discoveries enhance theoretical understanding and possess prospective applications in optimisation, numerical analysis, and diverse areas of applied mathematics. Furthermore, we enhance this work by discussing several special cases pertinent to this paper.