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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta Feb. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-01-0014 

Artículos

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

1 University Ismail Qemali Vlora, Dept. of Mathematics, Vlora, Albania. E-mail: artionkashuri@gmail.com

2 University Ismail Qemali Vlora, Dept. of Mathematics, Vlora, Albania. E-mail: rozanaliko86@gmail.com

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.

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

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Received: February 2019; Accepted: July 2019

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