SOME NEW HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES TO PRODUCTS OF TWO GENERALIZED (r; g, s,m,\phi)-PREINVEX FUNCTIONS

Abstract

In the present paper, a new class of generalized \((r; g, s, m, \varphi)\)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two generalized \((r; g, s, m, \varphi)\)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities to products of two generalized \((r; g, s, m, \varphi)\)-preinvex functions via Riemann-Liouville fractional integrals are established. These general inequalities give us some new estimates for the left-hand side of Gauss-Jacobi type quadrature formula and Hermite-Hadamard type fractional integral inequalities and also extend some results appeared in the literature (see [1]). Some conclusions and future research are also given.