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JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2021 Volume 10(28), Issue 1, Pages 3–22 (Mi pa313)

This article is cited in 3 papers

Several new integral inequalities via $k$-Riemann–Liouville fractional integrals operators

S. I. Butta, B. Bayraktarb, M. Umara

a COMSATS University Islamabad, Lahore Campus, Defence Road Off Raiwind Rd, Lda Avenue Phase 1 Lda Avenue, Lahore, Punjab 54000, Pakistan
b Bursa ULUDAĞ UNIVERSITY, Faculty of Education, Department of Mathematics and Science Education, Görukle Campus, 16059, BURSA, TURKEY

Abstract: The main objective of this paper is to establish several new integral inequalities including $k$-Riemann–Liouville fractional integrals for convex, $s$-Godunova–Levin convex functions, quasi-convex, $\eta$-quasi-convex. In order to obtain our results, we have used classical inequalities as Hölder inequality, Power mean inequality and Weighted Hölder inequality. We also give some applications.

Keywords: $\eta$-quasi-convex, $s$-Godunova–Levin type, $k$-Riemann–Liouville fractional integral, Hölder inequality, weighted Hölder inequality, power mean inequality.

UDC: 517.518.86, 517.218.244, 517.927.2

MSC: 26A33, 26A51, 26D15

Received: 22.07.2020
Revised: 30.11.2020
Accepted: 11.12.2020

Language: English

DOI: 10.15393/j3.art.2021.8770



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