Nonexpansive mappings defined on unbounded domains (Q884242)

The authors study the existence of fixed points for nonexpansive mappings when their domains are unbounded. The main result of this part of the article parallels a corresponding result due to \textit{R. E. Bruck jun.} [Trans. Am. Math. Soc. 179, 251--262 (1973; Zbl 0265.47043)] in the bounded case, and it relies heavily on the results of Bruck. Several fixed point theorems for nonexpansive mappings involve mappings \(f : C \to X\) in conjunction with boundary and inwardness conditions. It is customary in these results to assume that the domain \(C\) is bounded. Finally, the authors consider fixed point theorems for mappings \(f:C\to X\), where \(C\) is not necessarily bounded, which are nonexpansive or continuous pseudocontractive in conjunction with satisfy Leray-Schauder-type boundary conditions.