Petruşel, Adrian; Rus, Ioan A.; Şerban, Marcel-Adrian The role of equivalent metrics in fixed point theory. (English) Zbl 1278.54044 Topol. Methods Nonlinear Anal. 41, No. 1, 85-112 (2013). Several properties of maps and spaces are discussed with respect to the change of equivalent metric, especially those from metric fixed point theory, such as Picard operators, (generalized) contractions, and so on. Combined with a rich bibliography, the authors collect many results and examples from the literature, adding some new remarks and open questions. Reviewer: Zdzisław Dzedzej (Gdansk) Cited in 9 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems 47H04 Set-valued operators 47J25 Iterative procedures involving nonlinear operators 54E40 Special maps on metric spaces Keywords:fixed point theory; topologically equivalent metric; strongly equivalent metric; Picard operator; weakly Picard operator; contraction; generalizd contraction; well-posedness; shadowing property; stability; Ulam stability; invariant subset PDFBibTeX XMLCite \textit{A. Petruşel} et al., Topol. Methods Nonlinear Anal. 41, No. 1, 85--112 (2013; Zbl 1278.54044)