New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions
Date
2025
ISBN
Journal Title
Journal ISSN
Volume Title
Resource Type
Article
Publisher
University of Maragheh
Journal Title
New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions
Recommended by
Abstract
The main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for q-differentiable convex functions. These inequalities are useful for determining error bounds for the open Newton-Cotes formulas in both classical and q-calculus. This work distinguishes itself from existing studies by employing quantum operators, leading to sharper and more precise error estimates. These results extend the applicability of Newton-Cotes methods to quantum calculus, offering a novel contribution to the numerical analysis of convex functions. Finally, we provide mathematical examples and computational analysis to validate the newly established inequalities. © 2025 University of Maragheh. All rights reserved.
Description
Citation
Sahand Communications in Mathematical Analysis