SCOPUS 2025

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New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions
(University of Maragheh, 2025) Jarunee Soontharanon; Muhammad Aamir Ali; Shahram Rezapour; Muhammad Toseef; Thanin Sitthiwirattham; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; email: rezapourshahram@yahoo.ca
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.