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January 2018 Some different type integral inequalities concerning twice differentiable generalized relative semi-$(r; m, h)$-preinvex mappings
Artion Kashuri, Rozana Liko
Tbilisi Math. J. 11(1): 79-97 (January 2018). DOI: 10.2478/tmj-2018-0006

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.

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Artion Kashuri. Rozana Liko. "Some different type integral inequalities concerning twice differentiable generalized relative semi-$(r; m, h)$-preinvex mappings." Tbilisi Math. J. 11 (1) 79 - 97, January 2018. https://doi.org/10.2478/tmj-2018-0006

Information

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

zbMATH: 1384.26053
MathSciNet: MR3767424
Digital Object Identifier: 10.2478/tmj-2018-0006

Subjects:
Primary: 26A33
Secondary: 26D07, 26D10, 26D15

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences

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Vol.11 • No. 1 • January 2018
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