NEW CONVERGENCE DEFINITIONS FOR DOUBLE SEQUENCES IN g–METRIC SPACES


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GÜRDAL M., Kişi Ö., KOLANCI S.

Journal of Classical Analysis, cilt.21, sa.2, ss.173-185, 2023 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.7153/jca-2023-21-10
  • Dergi Adı: Journal of Classical Analysis
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.173-185
  • Anahtar Kelimeler: double sequence, g-metric spaces, statistical convergence, strongly Cesàro summability
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Süleyman Demirel Üniversitesi Adresli: Evet

Özet

In this paper, we define g-convergence and g-Cauchy of double sequences in g-metric spaces. Also we prove that g-limit is unique and every g-convergent double sequence is a g-Cauchy sequence. Additionally g-statistical convergence of double sequences is introduced and the theorem giving the relationship between statistical convergence and strongly Cesáro summability in a g-metric space is demonstrated. Further, we put forward the notations of g-lacunary statistical convergence and g-strongly lacunary convergence of double sequences and we also present some inclusion theorems.