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

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Soontharanon Jarunee; Ali Muhammad Aamir; Rezapour Shahram; Toseef Muhammad; Sitthiwirattham Thanin

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Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2025 | Volume:22 | Issue:1 Page(s): 205-219

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Title

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

Author(s)

Keywords

Open Newton-Cotes Formulas

Convex functions

q-Calculus

Fractional inequalities

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.

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