Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions

Hyder A., Budak H., Barakat M. A.

AIMS MATHEMATICS, cilt.9, sa.5, ss.11228-11246, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024551
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.11228-11246
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.