ON ABEL CONVERGENCE OF DOUBLE SEQUENCES

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Karaev M. T., Zeltser M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, cilt.31, sa.10, ss.1185-1189, 2010 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 31 Sayı: 10
• Basım Tarihi: 2010
• Doi Numarası: 10.1080/01630563.2010.501263
• Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.1185-1189
• Süleyman Demirel Üniversitesi Adresli: Hayır

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