New Approach to Weighted Newton-Type Inequalities Using Riemann–Liouville Fractional Integrals

Alqahtani R. T., BUDAK H.

Mathematical Methods in the Applied Sciences, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1002/mma.70636
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: bounded functions, convex functions, fractional integrals, functions of bounded variation, Lipschitzian functions, Newton-type inequalities
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this investigation paper, we present some weighted inequalities Newton-type for various classes of functions utilizing Riemann–Liouville fractional integrals. The study begins by introducing a positive weighted function to derive a key integral equality essential for proving the main results. By applying this equality along with Riemann–Liouville fractional integrals, we establish several weighted Newton-type inequalities for some function classes, including Lipschitzian functions, bounded functions, convex functions, and functions of bounded variation. The results offer valuable insights into the significance of inequalities of Newton-type and give some directions for future research. The findings extend those presented in earlier works.