ON ABEL CONVERGENCE OF DOUBLE SEQUENCES


Karaev M. T. , Zeltser M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, cilt.31, ss.1185-1189, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 31 Konu: 10
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1080/01630563.2010.501263
  • Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Sayfa Sayıları: ss.1185-1189

Özet

In terms of Berezin symbols, we give the concept of (Ber)-convergence of bounded double sequences. We prove that every (Ber)-convergent double sequence is Abel convergent. In particular, by using the Berezin symbols technique, we prove the following double sequence analog of the classical Abel theorem for the sequences: If the sequence {a(mn) }(infinity)(m,n=0) regularly converges to L, then