Generalization of different type integral inequalities for generalized (𝑠, 𝑚)-preinvex Godunova–Levin functions

Abstract

Abstract In the present paper, the notion of generalized ( s , m ) {(s,m)} -preinvex Godunova–Levin function of second kind is introduced, and some new integral inequalities involving generalized ( s , m ) {(s,m)} -preinvex Godunova–Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite–Hadamard, Ostrowski and Simpson type inequalities for generalized ( s , m ) {(s,m)} -preinvex Godunova–Levin functions of second kind via Riemann–Liouville fractional integral are established.