Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (r;s,m,varphi)-preinvex Functions

Artion Kashuri, Rozana Liko

Abstract


In the present paper, a new class of generalized $(r;s,m,\varphi)$-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized $(r;s,m,\varphi)$-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized $(r;s,m,\varphi)$-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see \cite{AkRl}, \cite{AkYil}), but also provide new estimates on these types.

Keywords


Hermite-Hadamard type inequality, H\"{o}lder's inequality, Minkowski's inequality, Cauchy's inequality, power mean inequality, Riemann-Liouville fractional integral, $s$-convex function in the second sense, $m$-invex, $P$-function.

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