Weighted fractional Euler–Maclaurin inequalities for convex and bounded variation functions via Riemann–Liouville integrals

Almoneef A. A., Hyder A., Hezenci F., BUDAK H.

Journal of Inequalities and Applications, vol.2025, no.1, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2025 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1186/s13660-025-03333-3
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Bounded variation, Differentiable convex functions, Euler–Maclaurin inequality, Riemann–Liouville integrals
  • Kocaeli University Affiliated: Yes

Abstract

This paper develops weighted Euler–Maclaurin-type inequalities using Riemann–Liouville fractional integrals for classes of differentiable convex functions and functions of bounded variation. The work begins with a foundational integral equality that incorporates a positive weighting function, which serves as the basis for constructing these Euler–Maclaurin-type inequalities. Through this approach, we derive specific fractional inequalities for convex functions and extend them to functions of bounded variation, addressing key accuracy bounds and demonstrating flexibility across applications. Some remarks and particular cases are discussed to provide deeper observation, showcasing variations of the derived inequalities under particular function classes and conditions. This exploration offers a comprehensive view of the potential extensions of weighted fractional inequalities within the context of fractional calculus.