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

Patterson R. F., Savaş E.

Filomat, vol.25, no.2, pp.129-135, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.2298/fil1102129p
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.129-135
  • Keywords: Double Sequences, Geometrically Dominated Double Sequences, Pringsheim convergent, Rate of Convergence
  • Uşak University Affiliated: No

Abstract

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.