Almost and Strongly Almost B(er,se,et,ue)−Summable Double Sequences

Tuğ, Orhan (2021) Almost and Strongly Almost B(er,se,et,ue)−Summable Double Sequences. Eurasian Journal of Science & Engineering, 7 (2). pp. 71-89. ISSN 2414-5602

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Abstract

In this paper, we define some new almost and strongly almost convergent double sequence spaces Be(Cf), Be(Cf0 ), Be[Cf ] and Be[Cf0 ] derived by the domain of four-dimensional sequential band matrix B(er,se,et,ue) in the spaces Cf , Cf0 , [Cf ] and [Cf0 ], respectively. Then we study some topological properties and prove some strict inclusion relations. Moreover, we calculate the α−,βbp− and γ−duals of the new spaces. Finally, we state some known lemmas concerning the four-dimensional matrix classes of almost convergent double sequences, then we characterize some new four-dimensional matrix transformations from and into the new sequence spaces Be(Cf) and Be[Cf ]. We conclude the paper with several significant results.

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