Matrix Transformations Involving Generalized Almost Convergent Sequences

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Atıf İçin Kopyala

SAVAŞ E., Zeltser M.

Analysis Mathematica, cilt.45, sa.2, ss.413-441, 2019 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 45 Sayı: 2
• Basım Tarihi: 2019
• Doi Numarası: 10.1007/s10476-019-0733-3
• Dergi Adı: Analysis Mathematica
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.413-441
• Anahtar Kelimeler: almost convergence, Maddox sequence space, matrix transformation
• Uşak Üniversitesi Adresli: Evet

Özet

In [7] Maddox generalized the spaces c0, c, ℓ1, ℓ∞ by adding powers pk (k ∈ ℕ) in the definitions of the spaces to the terms of the elements of the sequences (xk). Using the ideas of Maddox, Nanda [13] defined generalizations f(p) and f0(p) of the spaces of all almost convergent sequences f and of all sequences f0 almost convergent to 0. In [13] and [14] he characterized some classes of matrix transformations involving theses spaces and Maddox’s sequence spaces. We have discovered that almost all results in [13] and [14] are faulty. In this paper we give corresponding counterexamples and prove the correct results. Moreover we prove them in more general settings.