On generalized statistical and ideal convergence of metric-valued sequences

  • P. Das
  • E. Savaş

Abstract

We consider the notion of generalized density, namely, natural density of weight g recently introduced in [Balcerzak M., Das P., Filipczak M., Swaczyna J. Generalized kinds of density and the associated ideals // Acta Math. Hung. – 2015. –147, № 1. – P. 97 – 115] 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 more general form using the notion of ideals. The entire investigation is performed in the setting of general metric spaces extending the recent results of Kucukaslan M., Deger U., Dovgoshey O. On statistical convergence of metric valued sequences, see Ukr. Math. J. – 2014. – 66, № 5. – P. 712 – 720.
Published
25.12.2016
How to Cite
DasP., and SavaşE. “On Generalized Statistical and Ideal Convergence of Metric-Valued Sequences”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 12, Dec. 2016, pp. 1598-06, http://umj.imath.kiev.ua/index.php/umj/article/view/1946.
Section
Research articles