EXTENSION OF RIGHT-RADAU-TYPE INEQUALITIES TO FRACTAL SETS

Benchettah D. C., Meftah B., Saleh W., LAKHDARI A.

Palestine Journal of Mathematics, vol.14, no.3, pp.170-188, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2025
  • Journal Name: Palestine Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.170-188
  • Keywords: 2-point right-Radau formula, generalized convex functions, generalized Hölder inequality, generalized power mean inequality, local fractional integrals
  • Kocaeli University Affiliated: Yes

Abstract

In this study, we introduce a novel local fractional integral identity and utilize it to extend classical right-Radau-type inequalities to fractal sets. Addressing such inequalities poses a significant challenge due to their inherent asymmetry, which complicates their analysis and generalization. By leveraging the concept of generalized convexity within the framework of local fractional integrals, we successfully overcome this difficulty and derive refined results that generalize the 2-point right-Radau inequality. The theoretical advancements are complemented by a practical application, demonstrating the efficacy and versatility of our approach in fractal analysis.