Matrix Summability in Amenable Semigroups

Mah, Peter F.

doi:10.2307/2039170

Cited by 2 publications

(2 citation statements)

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“…Amenable semigroups were studied by [1]. The concept of summability in amenable semigroups was introduced in [15], [16]. In [3], Douglas extended the notion of arithmetic mean to amenable semigroups and obtained a characterization for almost convergence in amenable semigroups.…”

Section: It Can Be Shown Thatmentioning

confidence: 99%

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

Kı̇şı̇¹,

Çakal²

2018

ntmsci

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In this paper, the concepts of σ-uniform density of subsets A of the set N of positive integers and corresponding I σconvergence 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, λ ]-summability, σ-convergence and λ-statistical convergence of Folner sequences by using ideals and introduce new notions, namely, I σ-[V, λ ]-summability, I σ-λ-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-λ-statistical convergence of Folner sequences introduced by the author recently.

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Section: It Can Be Shown Thatmentioning

confidence: 99%

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

Kı̇şı̇¹,

Çakal²

2018

ntmsci

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show abstract

“…Nomika [23] showed that, if G is countable amenable group, there exists a sequence {S n } of finite subsets of Amenable semigroups were studied by [1]. The concept of summability in amenable semigroups was introduced in [13], [14]. In [3], Douglas extended the notion of arithmetic mean to amenable semigroups and obtained a characterization for almost convergence in amenable semigroups.…”

Section: Introductionmentioning

confidence: 99%