Some New Cauchy Sequence Spaces

Year 2018, Volume: 1 Issue: 4, 267 - 272, 20.12.2018

Harun Polat

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

Cited By: 1

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

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