Tbilisi Mathematical Journal

Some new $k$-fractional trapezium-like integral inequalities via generalized relative semi-$(r;m,h_{1},h_{2})$-preinvex mappings and applications

Artion Kashuri, Muhammad Adil Khan, and Rozana Liko

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Abstract

In this article, we first presented a new general identity concerning differentiable mappings defined on $m$-invex set via $k$-fractional integrals. By using the concept of generalized relative semi-$(r;m,h_{1},h_{2})$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to trapezium-like integral inequalities via $k$-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article. Applications to special means for trapezium-like integral inequalities via $k$-fractional integrals are provided as well.

Article information

Source
Tbilisi Math. J., Volume 12, Issue 3 (2019), 1-19.

Dates
Received: 11 February 2018
Accepted: 15 June 2019
First available in Project Euclid: 26 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1569463229

Digital Object Identifier
doi:10.32513/tbilisi/1569463229

Mathematical Reviews number (MathSciNet)
MR4012380

Zentralblatt MATH identifier
1396.26034

Subjects
Primary: 26A51: Convexity, generalizations
Secondary: 26A33: Fractional derivatives and integrals 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 Hölder's inequality Minkowski inequality power mean inequality $k$-fractional integrals $m$-invex

Citation

Kashuri, Artion; Khan, Muhammad Adil; Liko, Rozana. Some new $k$-fractional trapezium-like integral inequalities via generalized relative semi-$(r;m,h_{1},h_{2})$-preinvex mappings and applications. Tbilisi Math. J. 12 (2019), no. 3, 1--19. doi:10.32513/tbilisi/1569463229. https://projecteuclid.org/euclid.tbilisi/1569463229


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