On Generalized Statistical and Ideal Convergence of Metric-Valued Sequences

Das P., Savas E.

Ukrainian Mathematical Journal, vol.68, no.12, pp.1849-1859, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 12
  • Publication Date: 2017
  • Doi Number: 10.1007/s11253-017-1333-7
  • Journal Name: Ukrainian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1849-1859
  • Uşak University Affiliated: No

Abstract

We consider the notion of generalized density, namely, the natural density of weight g recently introduced in [M. Balcerzak, P. Das, M. Filipczak, and J. Swaczyna, Acta Math. Hung., 147, No. 1, 97–115 (2015)] and primarily study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequence under which the subsequence is also generalized statistically convergent. Some results are also obtained in a more general form by using the notion of ideals. The entire investigation is performed in the setting of general metric spaces extending the recent results of M. Kücükaslan, U. Deger, and O. Dovgoshey, [Ukr. Math. J., 66, No. 5, 712–720 (2014)].