On filter convergence of series

Leonov A., ORHAN C.

Real Analysis Exchange, cilt.40, sa.2, ss.459-474, 2015 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.14321/realanalexch.40.2.0459
  • Dergi Adı: Real Analysis Exchange
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.459-474
  • Anahtar Kelimeler: F-convergence, Filter, I-convergence, Ideal, Series, Statistical convergence
  • Ankara Üniversitesi Adresli: Evet

Özet

A series Σ xk is F-convergent to s if the sequence (Σk=1 n xk) of its partial sums is F-convergent to s. We describe filters F for which F- convergence of a series Σ xk implies F-convergence to 0 of the series terms xk. If (xk) is small enough with respect to a given filter F, then there is an F-subseries Σ k∈I xk that is absolutely convergent in the usual sense. Filters corresponding to summable ideals, Erdos-Ulam ideals, matrix summability ideals, lacunary ideals and Louveau-Veličković ideals are considered.