On I_{σ}-convergence of folner sequence on amenable semigroups

• Main Authors: Ömer Kişi, Burak Çakal
• Format: Article
• Language: English
• Published: BİSKA Bilisim Company 2018-07-01
• Series: New Trends in Mathematical Sciences
• Subjects: Folner sequence; amenable group; inferior; superior; I-convergence.
• Online Access: https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=8443

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.