A Novel Variant of Milne’s Rule Inequalities on Quantum Calculus for Convex Functions with Their Computational Analysis

Haider W., BUDAK H., Shehzadi A., Hezenci F., Chen H.

Journal of Nonlinear Modeling and Analysis, cilt.7, sa.5, ss.1727-1745, 2025 (Scopus) identifier

  • 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.