Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators

Abstract

Abstract In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of ψ-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and Hölder’s integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann–Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions.

Keywords

• h-convex function
• Riemann-Liouville fractional integrals
• ψ-Hilfer integral operator
• Hermite-Hadamard-Mercer inequality