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, cilt.2025, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1186/s13660-025-03333-3
  • Dergi Adı: Journal of Inequalities and Applications
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Bounded variation, Differentiable convex functions, Euler–Maclaurin inequality, Riemann–Liouville integrals
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.