Estimates involving the ω-Riemann-Liouville fractional integral operators by means of η-quasiconvexity with applications to means

Abstract

. Since not every quasiconvex function is convex, it is our purpose in this present paper to extend some already established inequalities of the Hermite–Hadamard–Fej´er type and its companions for convex functions to the class of η -quasiconvex functions. The new results obtained herein are in terms of the ω -Riemann–Liouville fractional integral operators and they reduce to inequalities for quasiconvex functions for a particular choice of the bifunction η . In addition, we apply some of our results to certain special means of positive real numbers to obtain more estimates in this regard.