On generalized statistical and ideal convergence of metric-valued sequences
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...
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| Date: | 2016 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2016
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1946 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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