Double sequence transformations that guarantee a given rate of P-convergence

Patterson R. F., Savaş E.

Filomat, cilt.25, sa.2, ss.129-135, 2011 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.2298/fil1102129p
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.129-135
  • Anahtar Kelimeler: Double Sequences, Geometrically Dominated Double Sequences, Pringsheim convergent, Rate of Convergence
  • Uşak Üniversitesi Adresli: Hayır

Özet

In this paper the following sequence space is presented. Let [t] be a positive double sequence and define the sequence space Ω″ (t) = {complex sequences x: Xk,l = O(tk,l)}. The set of geometrically dominated double sequences is defined as G″ = Ur,sε(0,1)G(r,s) where G(r,s) = {complex sequences x: xk,l = O(rksl)} for each r, s in the interval (0,1). Using this definition, four dimensional matrix characterizations of l∞,∞, c″ and c0″ into G″ and into Ω″ (t) are presented. In addition to these definitions and characterizations it should be noted that this ensure a rate of converges of at least as fast as [t]. Other natural implications will also be presented.