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

Authors

DOI:

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

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.

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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

Issue

Vol. 39 No. 1 (2020)

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Artículos

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How to Cite

[1]
“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, doi: 10.22199/issn.0717-6279-2020-01-0014.