On The Paranormed Spaces of Regularly Convergent Double Sequences

Basar F., Capan H.

RESULTS IN MATHEMATICS, cilt.72, ss.893-906, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00025-017-0693-5
  • Dergi Adı: RESULTS IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.893-906
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.