Inequalities for generalized Riemann–Liouville fractional integrals of generalized strongly convex functions

Abstract

Abstract Some new integral inequalities for strongly ( α , h − m ) $(\alpha ,h-m)$ -convex functions via generalized Riemann–Liouville fractional integrals are established. The outcomes of this paper provide refinements of some fractional integral inequalities for strongly convex, strongly m-convex, strongly ( α , m ) $(\alpha ,m)$ -convex, and strongly ( h − m ) $(h-m)$ -convex functions. Also, the refinements of error estimations of these inequalities are obtained by using two fractional integral identities. Moreover, using a parameter substitution and a constant multiplier, k-fractional versions of established inequalities are also given.

Keywords

• ( h − m ) $(h-m)$ -convex function
• Strongly ( h − m ) $(h-m)$ -convex function
• ( α , h − m ) $(\alpha, h-m)$ -convex function
• Strongly ( α , h − m ) $(\alpha, h-m)$ -convex function
• Hadamard inequality
• Riemann–Liouville fractional integrals