On I_{σ}-convergence of folner sequence on amenable semigroups
In this paper, the concepts of σ-uniform density of subsets A of the set N of positive integers and corresponding I_{σ}-convergence of functions defined on discrete countable amenable semigroups were introduced. Furthermore, for any Folner sequence inclusion relations between I_{σ}-convergence and i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
BİSKA Bilisim Company
2018-07-01
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| Series: | New Trends in Mathematical Sciences |
| Subjects: | |
| Online Access: | https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=8443 |
| Summary: | In this paper, the concepts of σ-uniform density of subsets A of the set N of positive integers and corresponding I_{σ}-convergence of functions defined on discrete countable amenable semigroups were introduced. Furthermore, for any Folner sequence inclusion relations between I_{σ}-convergence and invariant convergence also I_{σ}-convergence and [V_{σ}]_{p}-convergence were given. We introduce the concept of I_{σ}-statistical convergence and I_{σ}-lacunary statistical convergence of functions defined on discrete countable amenable semigroups. In addition to these definitions, we give some inclusion theorems. Also, we make a new approach to the notions of [V,\lamda]-summability,σ-convergence and σ-statistical convergence of Folner sequences by using ideals and introduce new notions, namely, I_{σ}-[V,\lamda]-summability, I_{σ}-\lamda-statistical convergence of Folner sequences. We mainly examine the relation between these two methods as also the relation between I_{σ}-statistical convergence and I_{σ}-\lamda-statistical convergence of Folner sequences introduced by the author recently. |
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| ISSN: | 2147-5520 2147-5520 |