### FIXED-CIRCLE PROBLEM ON *S*-METRIC SPACES WITH A GEOMETRIC VIEWPOINT

**DOI Number**

**First page**

**Last page**

#### Abstract

Recently, a new geometric approach called the fixed-circle problem has been introduced to fixed-point theory. The problem has been studied using different techniques on metric spaces. In this paper, we consider the fixed-circle problem on S-metric spaces. We investigate existence and uniqueness conditions for fixed circles of self-mappings on an <em>S</em>-metric space. Some examples of self-mappings having fixed circles are also given.

#### Keywords

#### Full Text:

PDF#### References

bibitem{Banach} S. Banach, Sur les operations dans les ensembles abstraits

et leur application aux equations integrals, textit{Fund. Math.} 2 (1922),

-181.

bibitem{Ciesielski-2007} K. Ciesielski, On Stefan Banach and some of his

results, textit{Banach J. Math. Anal.} 1 (2007), no.1, 1-10.

bibitem{Hieu} N. T. Hieu, N. T. Ly and N. V. Dung, A Generalization of

Ciric Quasi-Contractions for Maps on $S$-Metric Spaces, textit{Thai Journal

of Mathematics} 13 (2015), no.2, 369-380.

bibitem{Ozdemir-2011} N. "{O}zdemir, B. B. .{I}skender and N. Y. "{O}zg%

"{u}r, Complex valued neural network with M"{o}bius activation function,

textit{Commun. Nonlinear Sci. Numer. Simul.} 16 (2011), no.12, 4698-4703.

bibitem{nihal} N. Y. "{O}zg"{u}r and N. Tac{s}, Some fixed point

theorems on $S$-metric spaces{,} textit{Mat. Vesnik}{ 69} (2017), no.1,

-52.

bibitem{nihal2} N. Y. "{O}zg"{u}r and N. Tac{s}, Some new contractive

mappings on $S$-metric spaces and their relationships with the mapping $%

(S25) $, textit{Math. Sci.} 11 (2017), no.1, 7-16.

bibitem{nihal3} N. Y. "{O}zg"{u}r and N. Tac{s}, Some generalizations of

fixed point theorems on $S$-metric spaces, textit{Essays in Mathematics and

Its Applications in Honor of Vladimir Arnold}, New York, Springer, 2016.

bibitem{nihal4} N. Y. "{O}zg"{u}r and N. Tac{s}, Some fixed-circle

theorems on metric spaces, Bull. Malays. Math. Sci. Soc., (2017).

https://doi.org/10.1007/s40840-017-0555-z

bibitem{Ozgur-Aip} N. Y. "{O}zg"{u}r and N. Tac{s}, Some fixed-circle

theorems and discontinuity at fixed circle, AIP Conference Proceedings 1926,

(2018).

bibitem{Rhoades} B. E. Rhoades, A comparison of various definitions of

contractive mappings, textit{Trans. Amer. Math. Soc.} 226 (1977), 257-290.

bibitem{Sedghi-2012} S. Sedghi, N. Shobe and A. Aliouche, A Generalization

of Fixed Point Theorems in $S$-Metric Spaces, textit{Mat. Vesnik} 64

(2012), no.3, 258-266.

bibitem{Sedghi-2014} S. Sedghi and N. V. Dung, Fixed Point Theorems on $S$%

-Metric Spaces{,} textit{Mat. Vesnik}{ 66} (2014), no.1, 113-124.

bibitem{tez} N. Tac{s}, Fixed point theorems and their various

applications, Ph. D. Thesis, 2017.

DOI: https://doi.org/10.22190/FUMI1903459O

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)