Some New Cauchy Sequence Spaces

Harun POLAT

doi:https://doi.org/10.32323/ujma.399587

Article Details

Some New Cauchy Sequence Spaces

Authors:

Harun POLAT

Publisher:

Emrah Evren KARA

Main Topics:

Mathematics

Journal:

Universal Journal of Mathematics and Applications 2018 Vol.1 Issue 4, pp.267-272

Document Type:

Article

Publication Date:

12/2018

Document Language:

English

Document ID (Org No.):

2000670151

Frequency:

Quarterly

pISSN:

2619-9653

DOI:

https://doi.org/10.32323/ujma.399587

Abstract:

 


In this paper, our goal is to introduce some new Cauchy sequence spaces. These spaces are defined by Cauchy transforms. We shall use notations C∞(s,t)C∞(s,t)C_{\infty }\left( s,t\right) , C(s,t)C(s,t)C\left( s,t\right)  and C0(s,t) C0(s,t) C_{0}\left( s,t\right) ~for these new sequence spaces. We prove that these new sequence spaces C∞(s,t)C∞(s,t)C_{\infty }\left( s,t\right) , C(s,t)C(s,t)C\left( s,t\right)  and C0(s,t) C0(s,t) C_{0}\left( s,t\right) ~ are the BK−BK−BK-spaces and isomorphic to the spaces l∞l∞l_{\infty }, c c c\ and c0c0c_{0}, respectively. Besides the bases of these spaces, α−α−\alpha -, β− β− \beta -\ and γ−γ−\gamma - duals of these spaces will be given. Finally, the matrix classes (C(s,t):lp)(C(s,t):lp)(C\left( s,t\right) :l_{p}) and (C(s,t):c)(C(s,t):c)(C\left( s,t\right) :c) have been characterized.

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Article Details

Some New Cauchy Sequence Spaces

Authors: Harun POLAT

Publisher: Emrah Evren KARA

Main Topics: Mathematics

Journal: Universal Journal of Mathematics and Applications 2018 Vol.1 Issue 4, pp.267-272

Document Type: Article

Publication Date: 12/2018

Document Language: English

Document ID (Org No.): 2000670151

Frequency: Quarterly

pISSN: 2619-9653

DOI: https://doi.org/10.32323/ujma.399587

Issues

Authors:

Harun POLAT

Publisher:

Emrah Evren KARA

Main Topics:

Mathematics

Journal:

Universal Journal of Mathematics and Applications 2018 Vol.1 Issue 4, pp.267-272

Document Type:

Article

Publication Date:

12/2018

Document Language:

English

Document ID (Org No.):

2000670151

Frequency:

Quarterly

pISSN:

2619-9653

DOI:

https://doi.org/10.32323/ujma.399587