2019/09/01 by Orhan Tuǧ, Tug, Orhan
Mathematics · #Approximation Theory and Sequence Spaces
paper · pdf · doi:10.48550/arxiv.1909.00469
Most recently, some new double sequence spaces B(\Mu),\nB(\C\ϑ) where \ϑ= b,bp,r,f,f0 and\nB(\Lq) for 0<q<\∞ have been introduced as four-dimensional\ngeneralized difference matrix B(r,s,t,u) domain on the double sequence spaces\n\Mu, \C\ϑ where \ϑ= b,bp,r,f,f0 \nand \Lq for 0<q<\∞, and some topological properties, dual\nspaces, some new four-dimensional matrix classes and matrix transformations\nrelated to these spaces have also been studied by Tu ug and Ba csar and\nTu ug (see citeOT,OT2,Orhan,Orhan 2). In this present paper, we introduce\nnew strongly almost null and strongly almost convergent double sequence spaces\nB[\Cf] and B[\Cf0] as domain of four-dimensional\ngeneralized difference matrix B(r,s,t,u) in the spaces [\Cf] and\n[\Cf0], respectively. Firstly, we prove that the new double\nsequence spaces B[\Cf] and B[\Cf0] are Banach spaces\nwith its norm. Then, we give some inclusion relations including newly defined\nstrongly almost convergent double sequence spaces. Moreover, we calculate the\n\α-dual, \β(bp)-dual and \γ-dual of the space\nB[\Cf]. Finally, we characterize new four-dimensional matrix\nclasses ([\Cf];\Cf),\n([\Cf];\Mu), (B[\Cf];\Cf),\n(B[\Cf];\Mu) and we complete this work with some\nsignificant results.\n