NEW CONVERGENCE DEFINITIONS FOR DOUBLE SEQUENCES IN g–METRIC SPACES

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GÜRDAL M., Kişi Ö., KOLANCI S.

Journal of Classical Analysis, vol.21, no.2, pp.173-185, 2023 (Scopus)

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.7153/jca-2023-21-10
  • Journal Name: Journal of Classical Analysis
  • Journal Indexes: Scopus
  • Page Numbers: pp.173-185
  • Keywords: double sequence, g-metric spaces, statistical convergence, strongly Cesàro summability
  • Open Archive Collection: AVESIS Open Access Collection
  • Süleyman Demirel University Affiliated: Yes

Abstract

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.