A Novel Variant of Milne’s Rule Inequalities on Quantum Calculus for Convex Functions with Their Computational Analysis
Journal of Nonlinear Modeling and Analysis, cilt.7, sa.5, ss.1727-1745, 2025 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 7 Sayı: 5
- Basım Tarihi: 2025
- Doi Numarası: 10.12150/jnma.2025.1727
- Dergi Adı: Journal of Nonlinear Modeling and Analysis
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.1727-1745
- Anahtar Kelimeler: convex functions, Milne’s inequality, q-calculus
- Kocaeli Üniversitesi Adresli: Evet
Özet
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.