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

Authors

  • Akli Fundo Department of Mathematics, Polytechnic University of Tirana, Tirana, Albania
  • Artion Kashuri University of Vlora "Ismail Qemali", Department of Mathematics, Faculty of Technical Science, Albania
  • Miftar Ramosaco University of Vlora "Ismail Qemali", Department of Mathematics, Faculty of Technical Science, Albania
  • Rozana Liko University of Vlora "Ismail Qemali", Department of Mathematics, Faculty of Technical Science, Albania

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

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.

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Published

2017-07-11

Issue

Vol. 10 No. 4: (July 2017)

Section

Mathematical and Fuzzy Logic

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How to Cite

Some new Hermite-Hadamard Type Conformable Fractional Integral Inequalities for Twice Differentiable MT_(r;g,m,\varphi)-preinvex Functions. (2017). European Journal of Pure and Applied Mathematics, 10(4), 809-834. https://www.ejpam.com/index.php/ejpam/article/view/3048