Coincidence point theorems in some generalized metric spaces
DOI:
https://doi.org/10.24193/subbmath.2023.4.18Keywords:
dislocated metric space, semimetric space, singlevalued and multivalued mapping, comparison function, comparison pair, lower semi-continuity, coincidence point displacement functional, pre-weakly Picard mappingAbstract
Let \((X,d)\) be a complete dislocated metric space, \((Y,\rho)\) be a semimetric space and \(f,g:X\to Y\) be two mappings. We give some metric conditions which imply that the coincidence point set, \[C(f,g):=\{x\in X\ |\ f(x)=g(x)\}\not=\varnothing.\] Several coincidence point results are obtained for singlevalued and multivalued mappings.References
Berinde, V., Iterative Approximation of Fixed Points, Springer, 2007.
Berinde, V., Petru sel, A., Rus, I.A., Remarks on the terminology of the mappings in xed
point iterative methods, in metric spaces, Fixed Point Theory, 24(2023), no. 2, 525-540.
Blumenthal, L.M., Theory and Applications of Distance Geometry, Oxford, 1953.
Buic a, A., Principii de coincident a si aplicat ii, Presa Universitar a Clujean a, Cluj-
Napoca, 2001.
Filip, A.-D., Fixed Point Theory in Kasahara Spaces, Casa C art ii de S tiint a, Cluj-
Napoca, 2015.
Filip, A.-D., Conversion between generalized metric spaces and standard metric spaces
with applications in xed point theory, Carpathian J. Math., 37(2021), no. 2, 345-354.
Kirk, W.A., Sims, B., (eds.), Handbook of Metric Fixed Point Theory, Kluwer, 2001.
Petru sel, A., A generalization on Peetre-Rus theorem, Stud. Univ. Babe s-Bolyai Math.,
(1990), 81-85.
Petru sel, A., Rus, I.A., S erban, M.A., Basic problems of the metric xed point theory
and the relevance of a metric xed point theorem for a multivalued operator, J. Nonlinear
Convex Anal., 15(2014), 493-513.
Rus, I.A., Around metric coincidence point theory, Stud. Univ. Babe s-Bolyai Math.,
(2023), no. 2, 449-463.
Rus, I.A., Petru sel, A., Petru sel, G., Fixed Point Theory, Cluj Univ. Press, Cluj-Napoca,
Downloads
Additional Files
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
