Almost convergent sequence spaces derived by the domain of quadruple band matrix

Mustafa Cemil Bişgin

Almost convergent sequence spaces derived by the domain of quadruple band matrix

Source

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2020 > 19 > 155-170

Abstract

In this work, we construct the sequence spaces f(Q(r,s,t,u)), f0(Q(r,s,t,u)) and fs(Q(r,s,t,u)), where Q(r,s,t,u) is quadruple band matrix which generalizes the matrices Δ3, B(r,s,t), Δ2, B(r,s) and Δ, where Δ3, B(r,s,t), Δ2, B(r,s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β-, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

Identifiers

journal ISSN :

2300-133X

Authors

Mustafa Cemil Bişgin

Recep Tayyip Erdoğan University, Faculty Of Arts And Sciences, Department Of Mathematics

Keywords

matrix domain Schauder basis beta- and gamma-duals Banach Limits almost convergence and matrix classes

Additional information

Publication languages: English

Data set: DML

Publisher

Wydawnictwo Naukowe Uniwersytetu Pedagogicznego

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No field of science has been suggested yet.

Bibliography

Ahmad, Zaheer, and Mohammad Mursaleen. "Köthe-Toeplitz duals of some new sequence spaces and their matrix maps." Publ. Inst. Math. (Beograd) (N.S.) 42(56): 57-61.
Bektas, Çigdem Asma, and Rifat Çolak. "On the Köthe-Toeplitz duals of some generalized sets of difference sequences." Demonstratio Math. 33, no. 4 (2000): 797-803.
Basar, Feyzi, and Murat Kirisçi. "Almost convergence and generalized difference matrix." Comput. Math. Appl. 61, no. 3 (2011): 602-611.

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Mustafa Cemil Bişgin

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Bibliography

Ahmad, Zaheer, and Mohammad Mursaleen. "Köthe-Toeplitz duals of some new sequence spaces and their matrix maps." Publ. Inst. Math. (Beograd) (N.S.) 42(56): 57-61.

Bektas, Çigdem Asma, and Rifat Çolak. "On the Köthe-Toeplitz duals of some generalized sets of difference sequences." Demonstratio Math. 33, no. 4 (2000): 797-803.

Basar, Feyzi, and Murat Kirisçi. "Almost convergence and generalized difference matrix." Comput. Math. Appl. 61, no. 3 (2011): 602-611.

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Almost convergent sequence spaces derived by the domain of quadruple band matrix