Hermite-Hadamard-Mercer's-type Inequalities for $\mathfrak{h}$-convex function

Abstract

In this paper, we prove significant results related to the Hermite--Hadamard--Mercer-type inequality for h-convex functions in the framework of Katugampola fractional integral operators. Also, we establish some novel fractional inequalities related to the right and left sides of Hermite--Hadamard--Mercer-type inequalities for differentiable mappings whose derivatives in absolute value are h-convex function. The findings in this research generalise a number of inequities identified in earlier studies.