New perspectives on Euler-Maclaurin type inequalities via conformable fractional integrals

Set E., BUDAK H., ÇELİK B., Uzun N.

Filomat, cilt.39, sa.20, ss.7123-7135, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 20
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2520123s
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.7123-7135
  • Anahtar Kelimeler: conformable fractinal integrals, Convex functions, Euler-Maclaurin type inequalities
  • Marmara Üniversitesi Adresli: Evet

Özet

In this study, we have examined Euler-Maclaurin-type inequalities derived using conformable fractional integrals for various classes of functions. First, we have proved an integral equality that forms the basis of our main results. Then, we have presented Euler-Maclaurin-type inequalities for differentiable convex functions through conformable fractional integrals. Additionally, we have explored and established fractional Euler-Maclaurin-type inequalities for bounded functions and Lipschitzian functions. Our results have extended commonly used Simpson, Milne, and Newton-type integral inequalities, which are widely applied in mathematical analysis. Finally, we have discussed the potential implications of the results we have obtained via fractional integrals for future research.