ON ABEL CONVERGENCE OF DOUBLE SEQUENCES


Karaev M. T. , Zeltser M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.31, no.10, pp.1185-1189, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 10
  • Publication Date: 2010
  • Doi Number: 10.1080/01630563.2010.501263
  • Title of Journal : NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Page Numbers: pp.1185-1189

Abstract

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