Abstract
We study a space of nonlinear self-mappings of a complete metric space which is not necessarily bounded and show that a point of coincidence exists for a generic (typical) map.
References
- M. Abbas, G. Jungck: Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Analysis Appl. 341 (2008) 416–420.https://doi.org/10.1016/j.jmaa.2007.09.070Google Scholar
- S. Banach: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922) 133–181.https://doi.org/10.4064/fm-3-1-133-181Google Scholar
- C. Bargetz, E. Medjic: On the rate of convergence of iterated Bregman projections and of the alternating algorithm, J. Math. Analysis Appl. 481/1 (2020), art.no. 123482, 23p.https://doi.org/10.1016/j.jmaa.2019.123482Google Scholar
- R. Batra, S. Vashistha, R. Kumar: Coincidence point theorem for a new type of contraction on metric spaces, Int. J. Math. Analysis 8 (2014) 1315–1320.https://doi.org/10.12988/ijma.2014.45147Google Scholar
- R. K. Bisht: On coincidence and fixed points of general mappings, Linear Nonlinear Analysis 9 (2023) 207–212.Google Scholar
- Y. Censor, R. Davidi, G. T. Herman: Perturbation resilience and superiorization of iterative algorithms, Inverse Problems 26/6 (2010), art.no. 065008, 12p.https://doi.org/10.1088/0266-5611/26/6/065008Google Scholar
- Y. Censor, M. Zaknoon: Algorithms and convergence results of projection methods for inconsistent feasibility problems: a review, Pure Appl. Func. Analysis 3 (2018) 565–586.Google Scholar
- F. S. de Blasi, J. Myjak: Sur la convergence des approximations successives pour les contractions non linéaires dans un espace de Banach, C. R. Acad. Sci. Paris 283 (1976) 185–187.Google Scholar
- F. S. de Blasi, J. Myjak, S. Reich, A. J. Zaslavski: Generic existence and approximation of fixed points for nonexpansive set-valued maps, Set-Valued Var. Analysis 17 (2009) 97–112.https://doi.org/10.1007/s11228-009-0104-5Google Scholar
- W.-S. Du: Some generalizations of fixed point theorems of Caristi type and Mizoguchi-Takahashi type under relaxed conditions, Bull. Braz. Math. Soc. (N.S.) 50 (2019) 603–624.https://doi.org/10.1007/s00574-018-0117-5Google Scholar
- K. Goebel, W. A. Kirk: Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge (1990).https://doi.org/10.1017/CBO9780511526152Google Scholar
- K. Goebel, S. Reich: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, New York (1984).Google Scholar
- J. Jachymski: Extensions of the Dugundji-Granas and Nadler’s theorems on the continuity of fixed points, Pure Appl. Funct. Analysis 2 (2017) 657–666.Google Scholar
- G. Jungck: Commuting mappings and fixed points, Amer. Math. Monthly 83/4 (1976) 261–263.https://doi.org/10.1080/00029890.1976.11994093Google Scholar
- G. Jungck: Common fixed points for commuting and compatible maps in compacta, Proc. Amer. Math. Soc. 103 (1988) 977–983.https://doi.org/10.1090/S0002-9939-1988-0947693-2Google Scholar
- G. Jungck, S. Radenovic, S. Radojevic, V. Rakocevic: Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl. (2009), art.no. 643840, 13p.https://doi.org/10.1155/2009/643840Google Scholar
- E. Karapinar, Z. Mitrovic, A. Ozturk, S. Radenovic: On a theorem of Ciric in b-metric spaces, Rend. Circ. Mat. Palermo 70 (2021) 217–225.https://doi.org/10.1007/s12215-020-00491-9Google Scholar
- M. A. Khamsi, W. M. Kozlowski: Fixed Point Theory in Modular Function Spaces, Birkhäuser/Springer, Cham (2015).https://doi.org/10.1007/978-3-319-14051-3Google Scholar
- E. Rakotch: A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962) 459–465.https://doi.org/10.1090/S0002-9939-1962-0148046-1Google Scholar
- S. Reich: Genericity and porosity in nonlinear analysis and optimization, ESI Preprint 1756, Proc. CMS’05 (Computer Methods and Systems), Krakow (2005) 9–15.Google Scholar
- S. Reich, I. Shafrir: Nonexpansive iterations in hyperbolic spaces, Nonlinear Analysis 15 (1990) 537–558.https://doi.org/10.1016/0362-546X(90)90058-OGoogle Scholar
- S. Reich, A. J. Zaslavski: Genericity in Nonlinear Analysis, Developments in Mathematics Vol. 34, Springer, New York (2014).https://doi.org/10.1007/978-1-4614-9533-8Google Scholar
- F. Vetro, S. Radenovic: Some results of Perov type in rectangular cone metric spaces, J. Fixed Point Theory Appl. 20/1 (2018), art.no. 41, 16p.https://doi.org/10.1007/s11784-018-0520-yGoogle Scholar
- H.-K. Xu: Some random fixed point theorems for condensing and nonexpansive operators, Proc. Amer. Math. Soc. 110 (1990) 395–400.https://doi.org/10.1090/S0002-9939-1990-1021908-6Google Scholar
- H.-K. Xu: Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Problems 26(10 (2010), art.no. 105018, 17p.https://doi.org/10.1088/0266-5611/26/10/105018Google Scholar
- A. J. Zaslavski: Optimization on Metric and Normed Spaces, Springer Optimization and its Applications Vol. 44, Springer, New York (2010).https://doi.org/10.1007/978-0-387-88621-3Google Scholar
- A. J. Zaslavski: Approximate Solutions of Common Fixed Point Problems, Springer Optimization and Its Applications Vol. 112, Springer, Cham (2016).https://doi.org/10.1007/978-3-319-33255-0Google Scholar
- A. J. Zaslavski: Algorithms for Solving Common Fixed Point Problems, Springer Optimization and Its Applications Vol. 132, Springer, Cham (2018).https://doi.org/10.1007/978-3-319-77437-4Google Scholar
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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.
