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Convergence of approximating fixed point sets. (English) Zbl 0756.47042

Given a self-map \(f\) on a convex subset \(K\) of a Banach space \(X\) and a point \(y\in K\), the authors study the fixed point sets of the map \(f_{t,y}(x)=tf(x)+(1-t)y\) (\(0\leq t\leq 1\)), as well as their union over \(y\in K\). In particular, they give conditions under which this union converges, as \(t\to 1\), in the sense of Kuratowski, Wijsman, Hausdorff, Fisher, or Mosco.

MSC:

47H10 Fixed-point theorems
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