Asymptotic Wijsman -Deferred Statistical Equivalence

ULUSU U., Gülle E.

Proceedings of the National Academy of Sciences India Section A - Physical Sciences, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s40010-026-01101-6
  • Dergi Adı: Proceedings of the National Academy of Sciences India Section A - Physical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, MathSciNet, zbMATH, Technology Collection (ProQuest)
  • Anahtar Kelimeler: Asymptotic equivalence, Deferred Cesà ro mean, Double sequences of sets, Ideal-statistical convergence, Wijsman convergence
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

This paper introduces the notions of asymptotic Wijsman -deferred statistical equivalence and asymptotic Wijsman strong -deferred Cesàro equivalence for double sequences of sets in metric spaces. These concepts provide a unified framework that combines asymptotic equivalence, ideal-statistical convergence and deferred Cesàro summability within the Wijsman setting. We establish fundamental inclusion relations between the corresponding equivalence classes and prove that strong -deferred Cesàro equivalence implies -deferred statistical equivalence, while the converse holds under boundedness conditions. A counterexample is constructed to demonstrate that the reverse implication fails in general. Furthermore, we analyze the stability of these notions under suitable boundedness and structural constraints.