Tbilisi Mathematical Journal

Hermite-Hadamard type inequalities for generalized $(s, m, φ)$-preinvex functions via $k$-fractional integrals

Artion Kashuri and Rozana Liko

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Abstract

In the present paper, the notion of generalized $(s, m, φ)$-preinvex function is applied to establish some new Hermite-Hadamard type inequalities via $k$-fractional Riemann-Liouville integrals. At the end, some applications to special means are given. These results not only extend the results appeared in the literature, but also provide new estimates on these types.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 4 (2017), 73-82.

Dates
Received: 29 October 2016
Accepted: 20 September 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276059

Digital Object Identifier
doi:10.1515/tmj-2017-0046

Mathematical Reviews number (MathSciNet)
MR3717111

Zentralblatt MATH identifier
1375.26023

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 type inequality Hölder's inequality power mean inequality Riemann-Liouville fractional integral $s$-convex function in the second sense $m$-invex

Citation

Kashuri, Artion; Liko, Rozana. Hermite-Hadamard type inequalities for generalized $(s, m, φ)$-preinvex functions via $k$-fractional integrals. Tbilisi Math. J. 10 (2017), no. 4, 73--82. doi:10.1515/tmj-2017-0046. https://projecteuclid.org/euclid.tbilisi/1524276059


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