New perspectives on Milne’s rule inequalities with their computational analysis via quantum calculus

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

Applied Mathematics, cilt.40, sa.3, ss.687-700, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 3
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s11766-025-5210-0
  • Dergi Adı: Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.687-700
  • Anahtar Kelimeler: 26A51, 26D10, 26D15, convex functions, Milne’s inequality, q-calculus
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this study, we propose a novel method for establishing Milne’s rule-type inequalities within the context of quantum calculus applied to differentiable convex functions. Initially, we obtain a quantum integral identity, which serves as the foundation for deriving several new Milne’s rule inequalities tailored for quantum differentiable convex functions. These inequalities are particularly relevant in Open-Newton’s Cotes formulas, facilitating the determination of bounds for Milne’s rule in both classical and q-calculus domains. Additionally, we conduct computational analysis on these inequalities for convex functions and present mathematical examples and graphical representation to demonstrate the validity of our newly established results within the realm of q-calculus.