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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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