Extended Grüss type inequalities for generalized \((l,m)\)-fractional integrals with applications

Volume 40, Issue 1, pp 22--37 https://dx.doi.org/10.22436/jmcs.040.01.02

Publication Date: May 29, 2025 Submission Date: August 27, 2024 Revision Date: March 04, 2025 Accteptance Date: April 04, 2025

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Authors

M. Yousaf - Department of Mathematics \(\&\) Statistics, University of Southern Punjab, Bosan Road, Multan, Pakistan. S. Iqbal - Department of Mathematics \(\&\) Statistics, University of Southern Punjab, Bosan Road, Multan, Pakistan. M. Samraiz - Department of Mathematics, University of Sargodha, Sargodha, Pakistan. M. Vivas-Cortez - Pontificia Universidad Católica del Ecuador, Quito, Ecuador.

Abstract

The main motivation of this paper is to establish certain Grüss type inequalities by using the new generalized \((l,m)\)-Riemman-Liouville fractional integrals. We obtain the related results for the geometric, arithmetic, and harmonic \((l,m)\)-Riemman-Liouville fractional integrals as special cases of our general results. Also, we apply the Young's and Cauchy-Schwarz inequalities to obtain the variety of some related estimates. Our findings have potential applications in various fields of mathematical analysis and its related disciplines.

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Keywords

• Inequalities
• fractional integrals
• means
• kernel
• Young's inequality

MSC

•  26D10
•  26D15
•  26A33

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