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

Authors

  • Artion Kashuri University of Vlora "Ismail Qemali", Department of Mathematics, Vlora, Albania
  • Rozana Liko University of Vlora "Ismail Qemali", Department of Mathematics, Vlora, Albania

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.

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.

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Published

2017-04-20

Issue

Vol. 10 No. 3: (April 2017)

Section

Approximation Theory

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How to Cite

Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (r;s,m,varphi)-preinvex Functions. (2017). European Journal of Pure and Applied Mathematics, 10(3), 495-505. https://www.ejpam.com/index.php/ejpam/article/view/2996