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, vol.39, no.28, pp.10185-10204, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 28
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2528185b
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.10185-10204
  • Keywords: Bullen inequality, Milne inequality, Multiplicative absolute value, Multiplicative convex functions, Multiplicative fractional integrals
  • Kocaeli University Affiliated: No

Abstract

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.