Zur Bedeutung des Fixpunktsatzes von Schauder für die Fixpunkttheorie nicht notwendig kompakter Abbildungen. (German) Zbl 0561.47043

The author presents an approach to the fixed point theory, say, of condensing (limit compact) and semicontractive mappings by Schauder’s fixed point theorem. E.g., results of Darbo, Sadovskij, Danes et al. on the one hand and of Browder-Göhde-Kirk and Belluce-Kirk on the other hand fall into that scope. Moreover, the connectivity of the fixed point set of 1-set contractions is studied without degree theoretic methods, and an assertion of the Krasnosel’skij-Zabrejko-Petryshyn type is established. The concept of so-called quasi-compact mappings is introduced for dealing with the case, involving condensing mappings.
Reviewer: G.Hetzer


47H05 Monotone operators and generalizations
47H10 Fixed-point theorems