The spaces of B(r,s,t,u) strongly almost convergent double sequences and matrix transformations

Abstract

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 [1–4]). 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).