Some quantum corrected dual Euler-Simpson type inequalities for \(q\)-differentiable convex functions

Volume 40, Issue 4, pp 548--565 https://dx.doi.org/10.22436/jmcs.040.04.08

Publication Date: August 20, 2025 Submission Date: March 21, 2025 Revision Date: April 23, 2025 Accteptance Date: July 12, 2025

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Authors

A. Moumen - Department of Mathematics, Faculty of Sciences, University of Ha'il, Ha'il 55473, Saudi Arabia. R. Debbar - University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria. B. Meftah - Laboratory of Analysis and Control of Differential Equations , University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria. M. Bouye - Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia.

Abstract

The calculus of integrals is used to solve the majority of physics and engineering issues, which are frequently not immediately solved. This compels us to use approximation techniques, the selection of which is based on the class of functions that meet the necessary criteria as well as known points. Within the context of quantum calculus, we present an assessment of the error of the well-known corrected dual Euler-Simpson quadrature rule in this paper. As an auxiliary result, we create a new quantum identity. Using this identity, we prove several quantum-corrected dual Euler-Simpson type integral inequalities for functions with convex \(q\)-derivatives. We allow q to go towards \(1^{-}\) in order to obtain the classical inequalities. We provide a few applications to wrap up this research.

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Keywords

• Corrected dual Euler-Simpson inequality
• convex functions
• \(q\)-derivative
• \(q\)-integration

MSC

•  81P68
•  26D10
•  26A51

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