Hermite-Hadamard type fractional integral inequalities for products of two MT(r;g,m,φ)-preinvex functions

Keywords: Hermite-Hadamard type inequality, Hölder’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

A new class of MT(r;g,m,φ)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving products of two MT(r;g,m,φ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for products of two MT(r;g,m,φ)-preinvex functions via Riemann-Liouville fractional integrals are established. These general inequalities give us some new estimates for the left-hand side of Gauss-Jacobi type quadrature formula and Hermite-Hadamard type fractional integral inequalities. At the end, some conclusions and future research are given.

Author Biographies

Artion Kashuri, University Ismail Qemali Vlora.
Dept. of Mathematics.
Rozana Liko, University Ismail Qemali Vlora.
Dept. of Mathematics.

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Published
2020-02-04
How to Cite
[1]
A. Kashuri and R. Liko, “Hermite-Hadamard type fractional integral inequalities for products of two MT(r;g,m,φ)-preinvex functions ”, Proyecciones (Antofagasta, On line), vol. 39, no. 1, pp. 219-242, Feb. 2020.
Section
Artículos