Domain of Riesz mean in some spaces of double sequences
Indagationes Mathematicae, cilt.29, sa.3, ss.1009-1029, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 29 Sayı: 3
- Basım Tarihi: 2018
- Doi Numarası: 10.1016/j.indag.2018.03.006
- Dergi Adı: Indagationes Mathematicae
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1009-1029
- Anahtar Kelimeler: Summability theory, Double sequences, Double series, Alpha-, beta- and gamma-duals, Matrix domain of 4-dimensional matrices, Matrix transformations
- Uşak Üniversitesi Adresli: Evet
Özet
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.