Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Note on the structure of fixed point sets of $ 1$-set-contractions

Author: W. V. Petryshyn
Journal: Proc. Amer. Math. Soc. 31 (1972), 189-194
MathSciNet review: 0285944
Full-text PDF

Abstract | References | Additional Information

Abstract: Let $ X$ be a real Banach space, $ D$ a bounded open subset of $ X$, and $ T$ a demicompact $ 1$-set-contraction of the closure $ D$ into $ X$. It is shown that under certain conditions the set $ F(T)$ of fixed points of $ T$ in $ \bar D$ is a continuum (i.e., $ F(T)$ is a nonempty, compact and connected set).

References [Enhancements On Off] (What's this?)

Additional Information

Keywords: Structure of fixed point sets, continuum, measure of noncompactness, $ 1$-set-contractions, condensing, demicompact, generalized degree
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society