Some Hermite-Hadamard-Mercer Inequalities for General Fractional Convex on the Coordinates

Abstract

In this paper, we establish new Hermite-Hadamard-Mercer type inequalities for functions that are convex on the coordinates by employing the framework of generalized fractional integrals. Several integral identities are derived to obtain midpoint, trapezoidal, and Simpson-type inequalities as special cases. The presented results unify and extend numerous existing inequalities in convex analysis and fractional calculus, thereby providing a more general framework for further applications in numerical analysis, approximation theory, and optimization.