On generalized statistical and ideal convergence of metric-valued sequences - Das, P.; Savaş, E. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
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 resultsare also obtained in more general form using the notion of ideals. The entire investigation is performed in the setting ofgeneral metric spaces extending the recent results of Kucukaslan M., Deger U., Dovgoshey O. On statistical convergenceof metric valued sequences, see Ukr. Math. J. – 2014. – 66, № 5. – P. 712 – 720.