Weighted Fractional Euler–Maclaurin-Type Inequalities by Various Function Classes

Hezenci F., BUDAK H.

Experimental Mathematics, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/10586458.2025.2551929
  • Dergi Adı: Experimental Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: bounded functions Lipschitzian functions, convex functions, Euler–Maclaurin-type inequalities, functions of bounded variation
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, we establish weighted Euler-Maclaurin-type inequalities for various classes of functions by employing Riemann-Liouville fractional integrals. To begin with, we derive a fundamental integral identity using a positive weight function, which serves as the basis for our main results. Utilizing this identity in combination with Riemann-Liouville fractional integrals, we present several weighted Euler-Maclaurin-type inequalities that are applicable to a broad range of function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. These results offer a deeper understanding of Euler-Maclaurin-type inequalities and suggest potential avenues for future research. The findings presented herein extend and generalize previous results available in the literature.