Note on Abel Summability of Double Series

Yeşilkayagil M., Başar F.

Numerical Functional Analysis and Optimization, cilt.38, sa.8, ss.1069-1076, 2017 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 8
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/01630563.2017.1316991
  • Dergi Adı: Numerical Functional Analysis and Optimization
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1069-1076
  • Anahtar Kelimeler: Abel convergence of double sequence, double sequence, double series, Pringsheim convergence
  • Uşak Üniversitesi Adresli: Evet

Özet

In this paper, we prove that if a double series converges to α, then the power series Σi, jai, jxiyj converges for all x,y∈(0,1) and its sum is α, as x,y∈(1−, 1−). But the converse of this is not true, in general. Our main goal is to show that the converse of the idea, above, is true under which condition/conditions.