TY  - JOUR
T1  - An Overview of Triple-Composed $S$-Metric Spaces with Few Fixed-Point Theorems
AU  - Taş, Nihal
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.33401/fujma.1623200
JF  - Fundamental Journal of Mathematics and Applications
JO  - Fundam. J. Math. Appl.
PB  - Fuat USTA
WT  - DergiPark
SN  - 2645-8845
SP  - 169
EP  - 179
VL  - 8
IS  - 3
LA  - en
AB  - Metric fixed-point theory has received a lot of recent attention. The Banach fixed-point theorem served as the foundation for this theory. This theorem's generalizations have been looked at using various methodologies. One of these entails generalizing the prevalent contractive condition, while the other involves generalizing the prevalent metric space. Numerous generalized metric spaces were defined in the literature for the second generalization. As a new generalization of both a metric and an $S$-metric space in this context, our major goal is to present the idea of a triple-composed $S$% -metric space. We also provide some fundamental and topological ideas about triple-composed $S$-metric space. We look into some of this idea's characteristics. On triple-composed $S$-metric spaces, we demonstrate various fixed-point theorems. Finally, we provide the system of linear equations with an application.
KW  - Triple-composed $S$-metric
KW  - Banach contraction principle
KW  - Nemytskii-Edelstein
KW  - Fixed point
CR  - [1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 2 (1922), 133–181.
$ \href{https://eudml.org/doc/213289}{\mbox{[Web]}} $
CR  - [2] S.K. Chatterjea, Fixed-Point Theorems, C. R. Acad. Bulg. Sci., 25 (1972), 727–730.
CR  - [3] Lj. B. Ciric, Generalized contractions and fixed-point theorems, Publ. Inst. Math., 12(26) (1971), 19–26.
CR  - [4] M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc., 37 (1962), 74–79. $ \href{https://doi.org/10.1112/jlms/s1-37.1.74}{\mbox{[CrossRef]}} $
CR  - [5] G. Hardy and T. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16 (1973), 201–206. $ \href{https://doi.org/10.4153/CMB-1973-036-0}{\mbox{[CrossRef]}} $
CR  - [6] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71–76. $\href{https://doi.org/10.2307/2316437}{\mbox{[CrossRef]}}  $
CR  - [7] V.V. Nemytskii, The fixed point method in analysis, Uspekhi Mat. Nauk, 1 (1936), 141–174. $ \href{https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=5947&option_lang=eng}{\mbox{[Web]}} $
CR  - [8] S. Reich, Some remarks concerning contraction mappings, Canad. Math. Bull., 14 (1971), 121–122. $ \href{https://doi.org/10.4153/CMB-1971-024-9}{\mbox{[CrossRef]}}
 $
CR  - [9] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257–290. $\href{https://doi.org/10.1090/S0002-9947-1977-0433430-4}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/84968491333?origin=resultslist}{\mbox{[Scopus]}}  $
CR  - [10] V.M. Sehgal, On fixed and periodic points for a class of mappings, J. Lond. Math. Soc., 5(2) (1972), 571–576. $ \href{https://doi.org/10.1112/jlms/s2-5.3.571}{\mbox{[CrossRef]}} $
CR  - [11] I. Ayoob, N.Z. Chuan and N. Mlaiki, Double-Composed Metric Spaces, Mathematics, 11(8) (2023), 1866. $ \href{https://doi.org/10.3390/math11081866}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/85153743708?origin=resultslist}{\mbox{[Scopus]}}
 $
CR  - [12] İ. Demir, Fixed point theorems in complex valued fuzzy b-metric spaces with application to integral equations, Miskolc Math. Notes, 22(1)
(2021), 153–171. $\href{https://doi.org/10.18514/MMN.2021.3173}{\mbox{[CrossRef]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000661139500013}{\mbox{[Web of Science]}}  $
CR  - [13] N. Özgür and N. Taş, On S-metric spaces with some topological aspects, Electron. J. Math. Anal. Appl., 11(2) (2023), 1–8. $\href{https://doi.org/10.21608/ejmaa.2023.206319.1029}{\mbox{[CrossRef]}}  $
CR  - [14] S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64(3) (2012), 258–266.
$ \href{https://www.emis.de/journals/MV/123/mv12309.pdf}{\mbox{[Web]}} $
CR  - [15] S. Sedghi and N.V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik, 66(1) (2014), 113–124. $ \href{https://www.vesnik.math.rs/landing.php?name=mv14112&p=mv141.cap&utm_source=chatgpt.com}{\mbox{[Web]}}
\href{https://www.scopus.com/pages/publications/84888229460?origin=resultslist}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000436967600012}{\mbox{[Web of Science]}} $
CR  - [16] H. Aydi, N. Taş, N.Y. Özgür and N. Mlaiki, Fixed-discs in rectangular metric spaces, Symmetry, 11(2) (2019), 294. $ \href{https://doi.org/10.3390/sym11020294}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/85069818629?origin=resultslist}{\mbox{[Scopus]}} $
CR  - [17] H.A. Hammad, M.G. Alshehri and A. Shehata, Control functions in G-metric spaces: Novel methods for q-fixed points and q-fixed circles
with an application, Symmetry, 15(1) (2023), 164. $ \href{https://doi.org/10.3390/sym15010164}{\mbox{[CrossRef]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000920909100001}{\mbox{[Web of Science]}} $
CR  - [18] E. Kaplan, N. Mlaiki, N. Taş, S. Haque and A.K. Souayah, Some fixed-circle results with different auxiliary functions, J. Funct. Spaces,
(2022), 2775733. $ \href{https://doi.org/10.1155/2022/2775733}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/85132435513?origin=resultslist}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000813886100001}{\mbox{[Web of Science]}} $
CR  - [19] E. Kaplan, New fixed-circle results on fuzzy metric spaces with an application to dynamic market equilibrium, Mathematica Moravica, 27(1)
(2023), 73–83. $ \href{https://doi.org/10.5937/MatMor2301073K}{\mbox{[CrossRef]}} $
CR  - [20] N. Mlaiki, N. Özgür, N. Taş and D. Santina, On the fixed circle problem on metric spaces and related results, Axioms, 12(4) (2023), 401.
$ \href{https://doi.org/10.3390/axioms12040401}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/85153727582?origin=resultslist}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000980893400001}{\mbox{[Web of Science]}} $
CR  - [21] N.Y. Özgür and N. Taş, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc., 42(4) (2019), 1433–1449. $ \href{https://doi.org/10.1007/s40840-017-0555-z}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/85067400704?origin=resultslist}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000471896200010}{\mbox{[Web of Science]}}$
CR  - [22] N. Özgür, Fixed-disc results via simulation functions, Turkish J. Math., 43(6) (2019), 2794–2805. $ \href{https://doi.org/10.3906/mat-1812-44}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/pages/publications/85077596235?origin=resultslist}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000497971800011}{\mbox{[Web of Science]}} $
CR  - [23] N.Y. Özguür and N. Taş, Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Mathematical
Sciences, 11(1) (2017), 7–16. $ \href{https://doi.org/10.1007/s40096-016-0199-4}{\mbox{[CrossRef]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000400319900002}{\mbox{[Web of Science]}} $
UR  - https://doi.org/10.33401/fujma.1623200
L1  - https://dergipark.org.tr/en/download/article-file/4535239
ER  -