Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

Abstract

Abstract:In the present paper, by using new identity for fractional integrals some new estimates on generalizations of Hermite-Hadamard type inequalities for the class of generalized (s, m, ϕ)-preinvex functions via Riemann-Liouville fractional integral are established. These results not only extend the results appeared in the literature (see [2]), but also provide new estimates on these types. At the end, some applications to special means are given.Keywords: Hermite-Hadamard inequality, Hölder's inequality, power mean inequality, Riemann-Liouville fractional integral, s-convex in the second sense, m-invex, P-function.

Some New Ostrowski Type Inequalities Concerning Differentiable Generalized Relative Semi-(<i>r</i>; <i>m</i>, <i>p</i>, <i>q</i>, <i>h</i><SUB>1</SUB>, <i>h</i><SUB>2</SUB>)-Preinvex Mappings

“…Thus such inequalities were studied extensively by many researches and numerous generalizations, extensions and variants of them for various kind of functions like bounded variation, synchronous, Lipschitzian, monotonic, absolutely, continuous and n-times differentiable mappings etc. appeared in a number of papers [1][2][3][5][6][7][8][9][10]12,13,[15][16][17][18][19][20][21][22][23][24]26,29,30,31,36,37,38,40,43,45]. In numerical analysis many quadrature rules have been established to approximate the definite integrals [14,25,27,28,32,35,39,41].…”