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The spaces of B(r,s,t,u) strongly almost convergent double sequences and matrix transformations
Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2021-04-24 , DOI: 10.1016/j.bulsci.2021.102989
Orhan Tuǧ

Most recently, some new double sequence spaces B(Mu), B(Cϑ) where ϑ={b,bp,r,f,f0} and B(Lq) for 0<q< have been introduced as the domain of four-dimensional generalized difference matrix B(r,s,t,u) in the double sequence spaces Mu, Cϑ where ϑ={b,bp,r,f,f0} and Lq for 0<q<, and some topological properties, dual spaces, some new four-dimensional matrix classes and matrix transformations related to these spaces have also been studied by Tuğ and Başar and Tuğ (see [1], [2], [3], [4]). In this paper, we introduce new strongly almost convergent double sequence spaces B[Cf] and B[Cf0] whose B(r,s,t,u)-transforms are in the spaces [Cf] and [Cf0], respectively. The main body of this paper is designed by the investigation of the following hypothesis. Firstly, we examine some topological properties and inclusion relations including the new double sequence spaces B[Cf] and B[Cf0]. Also, we determine the α-dual, β(bp)-dual and γ-dual of the space B[Cf]. Finally, we give the necessary and sufficient conditions on an infinite matrix transforming from [Cf] over Cf, and we also characterize the classes ([Cf];Mu), (B[Cf];Cf) and (B[Cf];Mu).



中文翻译:

的空间[R 小号Ú)强烈几乎收敛双序列和矩阵变换

最近,一些新的双序列空间 中号üCϑ 在哪里 ϑ={bbp[RFF0}大号q 为了 0<q< 已作为四维广义差分矩阵的域引入 [RsŤü 在双序列空间 中号üCϑ 在哪里 ϑ={bbp[RFF0}大号q 为了 0<q<,Tuğ和Başar和Tuğ还研究了一些拓扑特性,对偶空间,一些新的三维矩阵类以及与这些空间有关的矩阵变换(请参见[1],[2],[3],[4] )。在本文中,我们介绍了新的强几乎收敛的双序列空间[CF][CF0] 谁的 [RsŤü-转换在空格中 [CF][CF0], 分别。本文的主体是通过以下假设的研究而设计的。首先,我们研究了一些拓扑特性和包含关系,包括新的双序列空间[CF][CF0]。此外,我们确定α-对偶,βbp对偶和γ对[CF]。最后,我们给出了从[CF] 超过 CF,并且我们还对类进行了表征 [CF];中号ü[CF];CF[CF];中号ü

更新日期:2021-04-28
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