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The role of equivalent metrics in fixed point theory. (English) Zbl 1278.54044

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.

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
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