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

Year 2017, Volume: 5 Issue: 2, 228 - 238, 15.10.2017

ARTION Kashurı , ROZANA Lıko

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.

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

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