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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0285944-9
MathSciNet review: 0285944
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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).


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Keywords: Structure of fixed point sets, continuum, measure of noncompactness, <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img14.gif" ALT="$1$">-set-contractions, condensing, demicompact, generalized degree
Article copyright: © Copyright 1972 American Mathematical Society