Coincidence and fixed points for maps on topological spaces. (English) Zbl 1132.54024

The author presents very elegant proofs based on quite new ideas of some new coincidence and fixed points theorems. For example instead of a metric he considers any symmetric distance function \(F(x,y)\) without triangle axiom. For any continuous mapping \(T:X\to X\) he considers the function \(F(x,T(x))\) and points \(w\) such that \(F(w,T(w))=inf \{F(x,T(x))| x\in K\}\), where \(K\) is a pseudo-compact subset of \(X\). Under corresponding conditions \(F(w,T(w))=0\) and so \(w\) is proved to be a fixed point.


54H25 Fixed-point and coincidence theorems (topological aspects)
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