Some new Hermite-Hadamard Type Conformable Fractional Integral Inequalities for Twice Differentiable MT_(r;g,m,\varphi)-preinvex Functions

Akli Fundo, Artion Kashuri, Miftar Ramosaco, Rozana Liko

Abstract

In the present paper, the notion of MT_(r;g,m,\varphi)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT_(r;g,m,\varphi)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT_(r;g,m,\varphi)-preinvex functions that are twice differentiable via conformable fractional integrals are established. At the end, some applications to special means are given.

Keywords

Hermite-Hadamard type inequality; MT-convex function; H\"{o}lder's inequality; power mean inequality; Minkowski inequality; Riemann-Liouville fractional integral; m-invex; P-function

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