Work

New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions

Year: 2025

Type: article

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.

Source: DOAJ (DOAJ: Directory of Open Access Journals)

Authors: Jarunee Soontharanon, Muhammad Ali, Shahram Rezapour, Muhammad Toseef, Thanin Sitthiwirattham

Institutions: King Mongkut's University of Technology North Bangkok, Nanjing Normal University, Azarbaijan Shahid Madani University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6888820861

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