Fixed point theorems for multivalued maps
Motivated by the recent work of \textit{A. Latif} and \textit{D.T. Luc} [Abstr. Appl. Anal. 2014, Article ID 104762, 5 p. (2014; \url{doi:10.1155/2014/104762})], the authors prove a fixed point theorem for multivalued maps with nonempty closed values in complete metric spaces. It is illustrated by an example that the theorem is more general than earlier known results. Moreover, this result is applied to show that under certain conditions every \(k\)-Lipschitz multivalued map defined on a closed convex subset of a Banach space has a fixed point, where \(k\) is possibly greater than 1.
scientific article; zbMATH DE number 6858706
scientific article