Domain of Riesz mean in some spaces of double sequences


YEŞİLKAYAGİL M., Basar F.

INDAGATIONES MATHEMATICAE-NEW SERIES, cilt.29, ss.1009-1029, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 29 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.indag.2018.03.006
  • Dergi Adı: INDAGATIONES MATHEMATICAE-NEW SERIES
  • Sayfa Sayıları: ss.1009-1029

Özet

In this study, we define the double sequence spaces (M-u)(Rqt), (Cp)(Rqt), (C-bp)(Rqt) and (C-r)(Rqt) as the domain of four dimensional Riesz mean R-qt in the spaces M-u, C-p, C-bp and C-r, respectively. Then, we examine some topological properties of those sequence spaces and we characterize the RH-regularity of the Riesz mean R-qt. Taking v is an element of{p, bp, r}, we determine the beta(v)-duals of the spaces (C-v)(Rqt) and we characterize the classes ((C-r)(Rqt) : C-v), (mu : (C-v)(Rqt)) and ((C-v)(Rqt) : C-f) of four-dimensional matrix transformations, where mu and C-f denote any given double sequence space and the space of almost convergent double sequences, respectively. (C) 2018 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).