ON ABEL CONVERGENCE OF DOUBLE SEQUENCES

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Karaev M. T., Zeltser M.

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

• Publication Type: Article / Article
• Volume: 31 Issue: 10
• Publication Date: 2010
• Doi Number: 10.1080/01630563.2010.501263
• Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1185-1189
• Süleyman Demirel University Affiliated: No

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