Domain of Riesz mean in some spaces of double sequences

Yeşilkayagil M., Başar F.

Indagationes Mathematicae, vol.29, no.3, pp.1009-1029, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1016/j.indag.2018.03.006
  • Journal Name: Indagationes Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1009-1029
  • Keywords: Alpha-, beta- and gamma-duals, Double sequences, Double series, Matrix domain of 4-dimensional matrices, Matrix transformations, Summability theory
  • Uşak University Affiliated: Yes

Abstract

In this study, we define the double sequence spaces (Mu)Rqt , (Cp)Rqt , (Cbp)Rqt and (Cr)Rqt as the domain of four dimensional Riesz mean Rqt in the spaces Mu, Cp, Cbp and Cr, respectively. Then, we examine some topological properties of those sequence spaces and we characterize the RH−regularity of the Riesz mean Rqt. Taking ϑ∈{p,bp,r}, we determine the β(ϑ)−duals of the spaces (Cϑ)Rqt and we characterize the classes ((Cr)Rqt :Cϑ), (μ:(Cϑ)Rqt ) and ((Cϑ)Rqt :Cf) of four-dimensional matrix transformations, where μ and Cf denote any given double sequence space and the space of almost convergent double sequences, respectively.