**Author: **Orhan Tuğ^{1 }

^{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.

**Published: December 22, 2021**

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