Around metric coincidence point theory
DOI:
https://doi.org/10.24193/subbmath.2023.2.18Keywords:
Metric space, singlevalued and multivalued mapping, coincidence point metric condition, fixed point metric condition, covering mapping, coincident point displacement, fixed point displacement, iterative approximation of coincidence point, iterative approximation of fixed point, weakly Picard mapping, pre-weakly Picard mapping, Ulam-Hyers stability, well-posedness of coincidence point problem.Abstract
In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, Teoria punctului fix ˆın analiza func¸tionala˘, Babe¸s- Bolyai Univ., Cluj-Napoca, 1973), A. Buic˘a (A. Buic˘a, Principii de coinciden¸ta ¸si aplica¸tii, Presa Univ. Clujean˘a, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, Covering 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¸sel (A. Petru¸sel, A generalization of Peetre-Rus theorem, Studia Univ. Babe¸s-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied.
Mathematics Subject Classification (2010): 54H25, 47H10, 47H04, 54C60, 47H09.
Received 04 January 2023; Accepted 01 March 2023.
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