Some asymptotic stationary point theorems in topological spaces
\textit{E. Tarafdar} and \textit{X.-Z. Yuan} introduced in [Appl. Math. Lett. 8, No. 6, 79--81 (1995; Zbl 0837.54011)] the notion of topological contraction and proved that every upper semicontinuous set-valued topological contraction with closed values on a compact topological space has a unique stationary point. In the paper under review, an asymptotic version of this result is derived and extended by relaxing compactness of the space. It is shown that any generalized sequence of iterations with an arbitrary initial point of a set-valued map on a complete first countable Hausdorff uniform space converges to its stationary point. Examples are given to distinguish these results from some known ones.
scientific article; zbMATH DE number 6092991
scientific article