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Normal structure and fixed points of nonexpansive maps in general topological spaces. (English) Zbl 1012.47030
The authors prove a well-known fixed point theorem of Kirk for nonexpansive maps in general topological spaces. They introduce the idea of \(p\)-normal structure and the notion of a \(t\)-symmetric function. Here \(t\) is the topology for the topological space. A set of suitable examples are given to illustrate the new terms introduced.
MSC:
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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