Some New Cauchy Sequence Spaces

Harun Polat

doi:10.32323/ujma.399587

EN

Some New Cauchy Sequence Spaces

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_{\infty }\left( s,t\right) $, $C\left( s,t\right) $ and $C_{0}\left( s,t\right) ~$for these new sequence spaces. We prove that these new sequence spaces $C_{\infty }\left( s,t\right) $, $C\left( s,t\right) $ and $C_{0}\left( s,t\right) ~$ are the $BK-$spaces and isomorphic to the spaces $l_{\infty }$, $c\ $and $c_{0}$, respectively. Besides the bases of these spaces, $\alpha -$, $\beta -\ $and $\gamma -$ duals of these spaces will be given. Finally, the matrix classes $(C\left( s,t\right) :l_{p})$ and $(C\left( s,t\right) :c)$ have been characterized.

Keywords

Cauchy sequence spaces,$\alpha -$,$~\beta -\ $and $% \gamma -$ duals,Schauder basis,Matrix mappings

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Harun Polat
Türkiye

Publication Date

December 20, 2018

Submission Date

February 28, 2018

Acceptance Date

April 6, 2018

Published in Issue

Year 2018 Volume: 1 Number: 4

DOI

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

IZ

https://izlik.org/JA97GY48WR

APA

Polat, H. (2018). Some New Cauchy Sequence Spaces. Universal Journal of Mathematics and Applications, 1(4), 267-272. https://doi.org/10.32323/ujma.399587

AMA

1.Polat H. Some New Cauchy Sequence Spaces. Univ. J. Math. Appl. 2018;1(4):267-272. doi:10.32323/ujma.399587

Chicago

Polat, Harun. 2018. “Some New Cauchy Sequence Spaces”. Universal Journal of Mathematics and Applications 1 (4): 267-72. https://doi.org/10.32323/ujma.399587.

EndNote

Polat H (December 1, 2018) Some New Cauchy Sequence Spaces. Universal Journal of Mathematics and Applications 1 4 267–272.

IEEE

[1]H. Polat, “Some New Cauchy Sequence Spaces”, Univ. J. Math. Appl., vol. 1, no. 4, pp. 267–272, Dec. 2018, doi: 10.32323/ujma.399587.

ISNAD

Polat, Harun. “Some New Cauchy Sequence Spaces”. Universal Journal of Mathematics and Applications 1/4 (December 1, 2018): 267-272. https://doi.org/10.32323/ujma.399587.

JAMA

1.Polat H. Some New Cauchy Sequence Spaces. Univ. J. Math. Appl. 2018;1:267–272.

MLA

Polat, Harun. “Some New Cauchy Sequence Spaces”. Universal Journal of Mathematics and Applications, vol. 1, no. 4, Dec. 2018, pp. 267-72, doi:10.32323/ujma.399587.

Vancouver

1.Harun Polat. Some New Cauchy Sequence Spaces. Univ. J. Math. Appl. 2018 Dec. 1;1(4):267-72. doi:10.32323/ujma.399587