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

Authors : ARTION KASHURI, ROZANA LIKO

Pages : 228-238

View : 17 | Download : 6

Publication Date : 2017-10-15

Article Type : Research Paper

Abstract :In the present paper, a new class of generalized $insert ignore into journalissuearticles values(s,m,\varphi);$-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized $insert ignore into journalissuearticles values(s,m,\varphi);$-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized $insert ignore into journalissuearticles values(s,m,\varphi);$-preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given.
Keywords : Hermite Hadamard type inequality, H\` o lder`s inequality, power mean inequality, Riemann Liouville fractional integral, s convex function in the second sense, m invex, P function