A novel perspective on the Bullen and Milne inequalities through the use of multiplicatively absolute value

Benaissa B., Azzouz N., BUDAK H., Kashuri A.

Filomat, cilt.39, sa.28, ss.10185-10204, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 28
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2528185b
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.10185-10204
  • Anahtar Kelimeler: Bullen inequality, Milne inequality, Multiplicative absolute value, Multiplicative convex functions, Multiplicative fractional integrals
  • Kocaeli Üniversitesi Adresli: Evet

Özet

This article formulates a new version of multiplicative Bullen and Milne inequalities derived from constraints on multiplicative Riemann-Liouville fractional integrals. We establish these further inequalities under the multiplicative absolute value and on the assumption that the function is multiplicatively h-convex. Additionally, these results are presented for multiplicatively P-functions and multiplicatively s-convex functions. The final section introduces a novel definition of a multiplicative Lipschitzian function, accompanied by examples, properties and theorems.