HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE GENERALIZED (s, m, ϕ)-PREINVEX FUNCTIONS

Abstract

In the present paper, a new class of generalized $(s,m,\varphi)$-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized $(s,m,\varphi)$-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized $(s,m,\varphi)$-preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given.