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

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1002/mma.70636
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Keywords: bounded functions, convex functions, fractional integrals, functions of bounded variation, Lipschitzian functions, Newton-type inequalities
  • Kocaeli University Affiliated: Yes

Abstract

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.