ON ABEL CONVERGENCE OF DOUBLE SEQUENCES


Karaev M. T., Zeltser M.

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

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