Note on the structure of fixed point sets of $1$-set-contractions
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- by W. V. Petryshyn
- Proc. Amer. Math. Soc. 31 (1972), 189-194
- DOI: https://doi.org/10.1090/S0002-9939-1972-0285944-9
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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).References
- Roger D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217–258. MR 312341, DOI 10.1007/BF02414948
- W. V. Petryshyn, Structure of the fixed points sets of $k$-set-contractions, Arch. Rational Mech. Anal. 40 (1970/71), 312–328. MR 273480, DOI 10.1007/BF00252680
- Massimo Furi and Alfonso Vignoli, A fixed point theorem in complete metric spaces, Boll. Un. Mat. Ital. (4) 2 (1969), 505–509. MR 0256378
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 189-194
- DOI: https://doi.org/10.1090/S0002-9939-1972-0285944-9
- MathSciNet review: 0285944