On The Paranormed Spaces of Regularly Convergent Double Sequences

In Hardy (Proc Camb Philos 19:86-95, 1916), Hardy defined the normed spaces C-r and C-ro of all regularly convergent and regularly null double sequences and made convergence factor calculations (i.e. some beta-dual calculations). In this paper, we extend these spaces to the paranormed spaces and C-r(t)and C-ro(t). Also, we define the paranormed spaces C-tr(t) and C-tro(t) of all totally regularly convergent and totally regularly null double sequences. We examine some topological properties of these spaces and determine their alpha-, beta- and gamma-duals