A Novel Variant of Milne’s Rule Inequalities on Quantum Calculus for Convex Functions with Their Computational Analysis
Journal of Nonlinear Modeling and Analysis, vol.7, no.5, pp.1727-1745, 2025 (Scopus)
- Publication Type: Article / Article
- Volume: 7 Issue: 5
- Publication Date: 2025
- Doi Number: 10.12150/jnma.2025.1727
- Journal Name: Journal of Nonlinear Modeling and Analysis
- Journal Indexes: Scopus
- Page Numbers: pp.1727-1745
- Keywords: convex functions, Milne’s inequality, q-calculus
- Kocaeli University Affiliated: Yes
Abstract
In this investigation, we introduce a novel approach for establishing Milne’s type inequalities in the context of quantum calculus for differentiable convex functions. First, we prove a quantum integral identity. We derive numerous new Milne’s rule inequalities for quantum differentiable convex functions. These inequalities are relevant in open Newton-Cotes formulas, as they facilitate the determination of bounds for Milne’s rule applicable to differentiable convex functions in both classical and q-calculus. In addition, we conduct a computational analysis of these inequalities for convex functions and provide mathematical examples to demonstrate the validity of the newly established results within the framework of q-calculus.