Almost and Strongly Almost B(r ̃,s ̃,t ̃,u ̃)- Summable Double Sequences

Author: Orhan Tuğ1
1 Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, Iraq

Abstract: In this paper, we define some new almost and strongly almost convergent double sequence spaces B ̃(C_f), B ̃(C_f0), B ̃[C_f] and B ̃[C_f0] derived by the domain of four-dimensional sequential band matrix B(r ̃,s ̃,t ̃,u ̃) in the spaces C_f, C_f0 , [C_f] and [C_f0 ], respectively. Then we study some topological properties and prove some strict inclusion relations. Moreover, we calculate α-,β(bp)- 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 B ̃(C_f), and B ̃[C_f]. We conclude the paper with several significant results.

Keywords: Four-dimensional band matrix, matrix domain, almost convergence, double sequences,
dual spaces, matrix transformations.

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Doi: 10.23918/eajse.v7i2p71

Published: December 22, 2021


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