APPROXIMATE FIXED POINT COMPUTATION VIA FCONTRACTION IN AMETRIC SPACES FOR HIGH-DIMENSIONAL DATA CLUSTERING
Abstract
In this study, we investigate Wardowski's contraction principle for F-contraction mappings and establish the existence and uniqueness of fixed points involving A-metric spaces. A F-contraction-based iterative method in an A-metric space is proposed and shown to converge to an approximate fixed point, demonstrating its e¤ectiveness for clustering in high-dimensional data.
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References
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[14] Sedghi, S, Shobe, N, Zhou, H: A common xed point theorem in Dmetric spaces. Fixed
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[15] Sedghi, S, Shobe, N, Aliouche, A: A generalization of xed point theorems in S-metric spaces.
Mat. Vesn. 64(3), 258-266 (2012)
[16] Piri, Hossein, and Poom Kumam. "Some xed point theorems concerning F-contraction in
complete metric spaces." Fixed point theory and applications 2014 (2014): 1-11
[17] Secelean, NA: Iterated function systems coinsisting of F-contractions. Fixed point theory and
applications. 2013. Article ID 277(2013).
intégrales. Fundam. Math. 3, 133-181 (1922)
[2] D. Wardowski, Fixed Points of a New Type of Contractive Mappings in Complete Metric
Spaces, Fixed Point Theory Appl. 2012 (2012), 94
[3] E. Karap¬nar, A. Fulga, R.P. Agarwal, A Survey: F-Contractions With Related Fixed Point
Results, J. Fixed Point Theory Appl. 22 (2020), 69. https://doi.org/10.1007/s11784-020-
00803-7.
[4] Fabiano, Nicola, et al. "On F-contractions: A survey." Contemporary Mathematics (2022):
327-342.
[5] Acar, Özlem, Aybala Sevde Özkapu, and Mahpeyker Öztürk. "Some xed point results on
ultrametric spaces endowed with a graph." Demonstratio Mathematica 57.1 (2024): 20230132.
[6] Bajovi´c, Duan, et al. "Remarks on Some Results of Extended Interpolative Hardy-Rogers-
Geraghty-Wardowski Contractions and ´C
iri´c-Reich-Rus Type F-Contractions." Sahand Com-
munications in Mathematical Analysis 22.1 (2025): 25-38.
[7] Abbas, Mujahid, Bashir Ali, and Yusuf I. Suleiman. "Generalized coupled common xed
point results in partially ordered A-metric spaces." Fixed point theory and applications 2015
(2015): 1-24.
[8] Gähler, S: 2-metriche raume und ihre topologische strukture. Math. Nachr. 26, 115-148 (1963)
[9] Dhage, BC: Generalized metric spaces mappings with xed point. Bull. Calcutta Math. Soc.
84, 329-336 (1992)
[10] Dhage, BC: A study of some xed point theorem. Ph.D. thesis, Marathwada University,
Aurangabad, India (1984)
[11] Naidu, SVR, Rao, KPR, Srinivasa, N: On the topology of D-metric spaces and the generation
of D-metric spaces from metric spaces. Int. J. Math. Math. Sci. 51, 2719-2740 (2004)
[12] Naidu, SVR, Rao, KPR, Srinivasa, N: On the concepts of balls in a D-metric space. Int. J.
Math. Math. Sci. 1, 133-141 (2005)
[13] Mustafa, Z, Sims, B: A new approach to generalized metric spaces. J. Nonlinear Convex Anal.
7(2), 289-297 (2006)
[14] Sedghi, S, Shobe, N, Zhou, H: A common xed point theorem in Dmetric spaces. Fixed
Point Theory Appl. 2007, Article ID 027906 (2007)
[15] Sedghi, S, Shobe, N, Aliouche, A: A generalization of xed point theorems in S-metric spaces.
Mat. Vesn. 64(3), 258-266 (2012)
[16] Piri, Hossein, and Poom Kumam. "Some xed point theorems concerning F-contraction in
complete metric spaces." Fixed point theory and applications 2014 (2014): 1-11
[17] Secelean, NA: Iterated function systems coinsisting of F-contractions. Fixed point theory and
applications. 2013. Article ID 277(2013).
Published
2026-03-15
Section
Special Issue: Advances in Nonlinear Analysis and Applications
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