Weighted Milne-type inequalities through Riemann-Liouville fractional integrals and diverse function classes

Almoneef A. A., Hyder A., Budak H.

AIMS MATHEMATICS, cilt.9, sa.7, ss.18417-18439, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 7
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024898
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.18417-18439
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

This research paper investigated weighted Milne-type inequalities utilizing RiemannLiouville fractional integrals across diverse function classes. A key contribution lies in the establishment of a fundamental integral equality, facilitated by the use of a nonnegative weighted function, which is pivotal for deriving the main results. The paper systematically proved weighted Milne-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. The obtained results not only contribute to the understanding of Milne-type inequalities but also offer insights that pave the way for potential future research in the considered topics. Furthermore, it is evident that the results obtained encompass numerous findings that were previously presented in various studies as special cases.