APPROXIMATE FIXED POINT COMPUTATION VIA Fô€€€CONTRACTION IN Aô€€€METRIC SPACES FOR HIGH-DIMENSIONAL DATA CLUSTERING
DOI:
https://doi.org/10.5269/bspm.79894Abstract
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.
References
[1] Banach, B: Sur les opérations dons les ensembles abstraits et leur application aux équations
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, Dušan, 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 Dô€€€metric 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).
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, Dušan, 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 Dô€€€metric 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).
Downloads
Published
2026-03-15
Issue
Section
Conf. Issue: Advances in Nonlinear Analysis and Applications
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
