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

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.