Abstract
Let $(X,d)$ be a complete metric space, $(Y,\rho)$ be a metric space and $f,g:X\to Y$ be two mappings. The problem is to give metric conditions which imply that, $C(f,g):=\{x\in X\ |\ f(x)=g(x)\}\not=\emptyset$. In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, \emph{Teoria punctului fix \^in analiza func\c tional\u a}, Babe\c s-Bolyai Univ., Cluj-Napoca, 1973), A. Buic\u a (A. Buic\u a, \emph{Principii de coinciden\c t\u a \c si aplica\c tii}, Presa Univ. Clujean\u a, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, \emph{Co\-vering mappings in metric spaces and fixed points}, Dokl. Math., 76(2007), no.2, 665-668) appear as corollaries. In the case of multivalued mappings our result generalizes some results given by A.V. Arutyunov and by A. Petru\c sel (A. Petru\c sel, \emph{A generalization of Peetre-Rus theorem}, Studia Univ. Babe\c s-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied.
Reference55 articles.
1. "[1] Aamri, M., Chaira, K., Approximation du point fixe et applications faiblement contractantes, Extracta Mathematicae, 17(2002), no. 1, 97-110.
2. [2] Aldea, F., Buică, A., On Peetre's condition in the coincidence theory, Proceed. Seminar T. Popoviciu, Cluj-Napoca, 2000, 1-8.
3. [3] Angrisani, M., Clavelli, M., Synthetic approaches to problems of fixed points in metric space, Ann. Mat. Pura ed Appl., 170(1996), 1-12. DOI: https://doi.org/10.1007/bf01758980.
4. [4] Anisiu, M.-C., Point-to-set mappings. Continuity, Sem. Fixed Point Theory, Preprint Nr. 3(1981), Babeș-Bolyai Univ., Cluj-Napoca, 1-100.
5. [5] Arutyunov, A.V., Covering mappings in metric spaces and fixed points, Doklady Math., 76(2007), no. 2, 665-668. DOI: https://doi.org/10.1134/s1064562407050079.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献