Tbilisi Mathematical Journal

Some different type integral inequalities concerning twice differentiable generalized relative semi-$(r; m, h)$-preinvex mappings

Artion Kashuri and Rozana Liko

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Abstract

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-$(r; m, h)$-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on $m$-invex set is derived. By using the notion of generalized relative semi-$(r; m, h)$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 1 (2018), 79-97.

Dates
Received: 10 September 2017
Accepted: 25 December 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276032

Digital Object Identifier
doi:10.2478/tmj-2018-0006

Mathematical Reviews number (MathSciNet)
MR3767424

Zentralblatt MATH identifier
1384.26053

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 26D07: Inequalities involving other types of functions 26D10: Inequalities involving derivatives and differential and integral operators 26D15: Inequalities for sums, series and integrals

Keywords
Hermite-Hadamard inequality Ostrowski inequality Simpson inequality Hölder's inequality power mean inequality Minkowski inequality fractional integrals $m$-invex

Citation

Kashuri, Artion; Liko, Rozana. Some different type integral inequalities concerning twice differentiable generalized relative semi-$(r; m, h)$-preinvex mappings. Tbilisi Math. J. 11 (2018), no. 1, 79--97. doi:10.2478/tmj-2018-0006. https://projecteuclid.org/euclid.tbilisi/1524276032


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