On continuity of fixed points of collectively condensing maps
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- by Martin Fan Cheng PDF
- Proc. Amer. Math. Soc. 63 (1977), 74-76 Request permission
Abstract:
In this paper, we prove, in two parts, the following claim. Let X be a Banach space and $\Lambda$ an arbitrary topological space. Suppose that $T:\Lambda \times X \to X$ is collectively condensing; then the fixed point set $S(\lambda ,y)$ has closed graph if and only if T is continuous in both $\lambda$ and y.References
- Zvi Artstein, On continuous dependence of fixed points of condensing maps, Dynamical systems (Proc. Internat. Sympos., Brown Univ., Providence, R.I., 1974) Academic Press, New York, 1976, pp. 73–75. MR 0636801
- Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 74-76
- MSC: Primary 47H10; Secondary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0435943-3
- MathSciNet review: 0435943