A note on attractors for compact sets
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- by J. L. Solomon PDF
- Proc. Amer. Math. Soc. 65 (1977), 293-296 Request permission
Abstract:
Let G be a closed convex subset of a Banach space $X,f:G \to G$ a continuous map and $M \subset G$ an attractor for compact sets under f. It is shown that if M is not connected, then M has a unique invariant component which is an attractor for points; moreover, for each x in G, the set of subsequential limit points of x under f is a subset of this unique invariant component.References
- L. F. Guseman Jr. and J. L. Solomon, Subsequential limit points of successive approximations, Proc. Amer. Math. Soc. 34 (1972), 573–577. MR 298640, DOI 10.1090/S0002-9939-1972-0298640-9
- F. T. Metcalf and T. D. Rogers, The cluster set of sequences of successive approximations, J. Math. Anal. Appl. 31 (1970), 206–212. MR 264147, DOI 10.1016/0022-247X(70)90132-0
- Roger D. Nussbaum, Some asymptotic fixed point theorems, Trans. Amer. Math. Soc. 171 (1972), 349–375. MR 310719, DOI 10.1090/S0002-9947-1972-0310719-6
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 293-296
- MSC: Primary 47H99; Secondary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0637100-4
- MathSciNet review: 0637100