FIXED-CIRCLE AND FIXED-DISC PROBLEM IN METRIC SPACES
Keywords:
fixed circle, fixed disk
Abstract
In this paper, we give certain existence theorems using different type of contraction for
fixed circles and fixed disc results of self-mapping on metric spaces. Also, we give some necessary
examples to show the validity of our theoretical results.
References
[1] O¨ zgu¨r, N. Y. and Tas¸, N. Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. 42(4)
(2019), 1433-1449.
[2] O¨ zgu¨r, N., and Tas¸, N. On The Geometry of ϕ-Fixed Points. Conference Proceedings Of Science And Technology.
4(2) (2021), 226-231.
[3] O¨ zgu¨r, N., and Tas¸, N. Geometric properties of fixed points and simulation functions. arXiv preprint
arXiv:2102.05417. (2021) Feb 10.
[4] Karapınar E. Fixed points results via simulation functions. Filomat. 30(8) (2016) 2343-2350.
[5] O¨ zgu¨r, N. Fixed-disc results via simulation functions, Turkish J. Math. 43(6), (2019) 2794-2805.
[6] Tas¸, N. Mlaiki N., Aydi H.,O¨ zgu¨r N. Fixed-disc results on metric spaces, Filomat 35(2) (2021) 447–457
[7] Tas¸, N., O¨ zgu¨r, N.Y. Mlaiki, N. New types of Fc-contractions and the fixed-circle problem. Mathematics 6
(2018) 188.
[8] Mlaiki, N., O¨ zgu¨r, N., Tas¸, N., and Santina, D. On the Fixed Circle Problem on Metric Spaces and Related
Results. Axioms 12(4) (2023) 401.
[9] Tas¸ N. Various types of fixed-point theorems on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. December
20(2) (2018) 211-223. doi:10.25092/baunfbed.426665
[10] O¨ zgu¨r, N.Y. Tas¸, N. C¸ elik, U. New fixed-circle results on S-metric spaces. Bull. Math. Anal. Appl. 9 (2017)
10–23.
[11] O¨ zgu¨r, N.Y., Tas¸, N. Fixed-circle problem on S-metric spaces with a geometric viewpoint. Facta Univ. (NIS)
Ser. Math. Inform. 34 (2019) 459–472.
(2019), 1433-1449.
[2] O¨ zgu¨r, N., and Tas¸, N. On The Geometry of ϕ-Fixed Points. Conference Proceedings Of Science And Technology.
4(2) (2021), 226-231.
[3] O¨ zgu¨r, N., and Tas¸, N. Geometric properties of fixed points and simulation functions. arXiv preprint
arXiv:2102.05417. (2021) Feb 10.
[4] Karapınar E. Fixed points results via simulation functions. Filomat. 30(8) (2016) 2343-2350.
[5] O¨ zgu¨r, N. Fixed-disc results via simulation functions, Turkish J. Math. 43(6), (2019) 2794-2805.
[6] Tas¸, N. Mlaiki N., Aydi H.,O¨ zgu¨r N. Fixed-disc results on metric spaces, Filomat 35(2) (2021) 447–457
[7] Tas¸, N., O¨ zgu¨r, N.Y. Mlaiki, N. New types of Fc-contractions and the fixed-circle problem. Mathematics 6
(2018) 188.
[8] Mlaiki, N., O¨ zgu¨r, N., Tas¸, N., and Santina, D. On the Fixed Circle Problem on Metric Spaces and Related
Results. Axioms 12(4) (2023) 401.
[9] Tas¸ N. Various types of fixed-point theorems on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. December
20(2) (2018) 211-223. doi:10.25092/baunfbed.426665
[10] O¨ zgu¨r, N.Y. Tas¸, N. C¸ elik, U. New fixed-circle results on S-metric spaces. Bull. Math. Anal. Appl. 9 (2017)
10–23.
[11] O¨ zgu¨r, N.Y., Tas¸, N. Fixed-circle problem on S-metric spaces with a geometric viewpoint. Facta Univ. (NIS)
Ser. Math. Inform. 34 (2019) 459–472.
Published
2025/12/17
Section
Original Scientific Papers
Copyright (c) 2025 Uma Patel
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