Around metric coincidence point theory - RUS, Ioan A. (Studia Universitatis Babeș-Bolyai Mathematica, 2023)
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.