# On the topological equivalence of S-metric and cone S-metric spaces

@inproceedings{Tacs2017OnTT, title={On the topological equivalence of S-metric and cone S-metric spaces}, author={Nihal Tacs}, year={2017} }

The aim of this paper is to establish the equivalence between the concepts of an S-metric space and a cone S-metric space using some topological approaches. We introduce a new notion of TV S-cone S-metric space using some facts about topological vector spaces. We see that the known results on cone S-metric spaces (or N -cone metric spaces) can be directly obtained from the studies on S-metric spaces.

## References

SHOWING 1-10 OF 20 REFERENCES

Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25)

- Mathematics
- 2017

Recently, S-metric spaces are introduced as a generalization of metric spaces. In this paper, we consider the relationships between of an S-metric space and a metric space, and give an example of an…

A note on the equivalence of some metric and cone metric fixed point results

- Mathematics, Computer ScienceAppl. Math. Lett.
- 2011

This work establishes the equivalence between some fixed point results in metric and in (topological vector space) cone metric spaces, and achieves a common fixed point theorem for f -quasicontractions.

On the metrizability of cone metric spaces

- Mathematics
- 2011

Abstract We have shown in this paper that a (complete) cone metric space ( X , E , P , d ) is indeed (completely) metrizable for a suitable metric D. Moreover, given any finite number of contractions…

Cyclic Contraction on S- Metric Space

- Mathematics
- 2013

In this paper we introduced the concepts of cyclic contraction on S- metric space and proved some fixed point theorems on S- metric space. Our presented results are proper generalization of Sedghi et…

A generalization of fixed point theorems in $S$-metric spaces

- Mathematics
- 2012

In this paper, we introduce S-metric spaces and give some of their properties. Also we prove a fixed point theorem for a self-mapping on a complete S-metric space.

On the end of the cone metric spaces

- Mathematics
- 2014

Abstract Starting with the initial paper of Huang and Zhang [2] in 2007, more than six hundred papers dealing with cone metric spaces have been published so far. In this short note we present a…

A Generalization of Ciric Quasi-Contractions for Maps on S-Metric Spaces

- Mathematics
- 2014

In this paper, we prove a fixed point theorem for a class of maps on S-metric spaces. As applications, we get the fixed point theorems in [1] and [2]. Also, examples are given to analyze the results.

Cone S-Metric Space and Fixed Point Theorems of Contractive Mappings

- Mathematics
- 2017

In this paper, we discuss the concept of generalize d -Metric space of Cone Metric space and prove some contractive conditions of unique fixed point.

Some Generalizations of Fixed-Point Theorems on S-MetricSpaces

- Mathematics
- 2016

In this paper we prove new fixed-point theorems on complete S-metric spaces. Our results generalize and extend some fixed-point theorems in the literature. We give some examples to show the validity…

A note on cone metric fixed point theory and its equivalence

- Mathematics
- 2010

Abstract The main aim of this paper is to investigate the equivalence of vectorial versions of fixed point theorems in generalized cone metric spaces and scalar versions of fixed point theorems in…