Deferred weighted diagonal upgrade principles for windowed statistical convergence: external ideals and frequent cauchy behavior

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GÜRDAL M., Kişi Ö.

Journal of Applied Mathematics and Computing, cilt.72, sa.7, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72 Sayı: 7
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s12190-026-02850-8
  • Dergi Adı: Journal of Applied Mathematics and Computing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Compendex, INSPEC, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: Deferred weighted statistical convergence, Diagonal statistical pre-cauchy, Frequent cauchy, Fubini-type ideal, Ideal cauchy sequence, Ideal convergence, Moving-window summability, Windowed approximation
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Süleyman Demirel Üniversitesi Adresli: Evet

Özet

Let be a fixed admissible ideal on and let be a deferred window scheme equipped with positive weights. Using the associated window proportions and the square/rectangular pair counts and, we define -deferred weighted statistical convergence, its diagonal statistically pre-Cauchy variant, and the corresponding -deferred weighted frequent Cauchy property on. We first prove that -deferred weighted statistical convergence always yields -deferred weighted frequent Cauchy behavior. Our main upgrade theorem (Theorem 4.4) shows that, for bounded sequences, diagonal pairwise control can be promoted to -deferred weighted statistical convergence provided that the deferred weighted window means form an -convergent sequence; in particular, it suffices that the mean sequence is -Cauchy in. Examples show that diagonal testing alone cannot replace the full rectangular scheme and that the mean-coherence assumption is essential.