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)

 
 

 

A note on Kellogg's uniqueness theorem for fixed points


Author: Louis A. Talman
Journal: Proc. Amer. Math. Soc. 69 (1978), 248-250
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1978-0467416-7
MathSciNet review: 0467416
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In 1975, R. B. Kellogg gave a condition guaranteeing uniqueness for the fixed point whose existence is insured by the Schauder Theorem. In this note, we indicate how to extend Kellogg's result to the class of k-set-contractions.


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

  • [1] R. B. Kellogg, Uniqueness in the Schauder fixed point theorem, Proc. Amer. Math. Soc. 60 (1976), 207-210. MR 0423137 (54:11118)
  • [2] M. A. Krasnosel'skii, Topological methods in the theory of non-linear integral equations, GITTL, Moscow, 1956; English transl., Macmillan, New York, 1964. MR 0096983 (20:3464)
  • [3] R. H. Martin, Non-linear operators and differential equations in Banach spaces, Wiley, New York, 1976. MR 0492671 (58:11753)
  • [4] R. D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 37 (1970), 473-478. MR 0264434 (41:9028)
  • [5] -, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. 89 (1971), 217-258. MR 0312341 (47:903)
  • [6] B. N. Sadovskii, Limit-compact and condensing operators, Uspehi Mat. Nauk 27 (1972), 81-146 = Russian Math. Surveys 27 (1972), 85-155. MR 0428132 (55:1161)
  • [7] C. A. Stuart and J. F. Toland, The fixed point index of a linear k-set-contraction, J. London Math. Soc. (2) 6 (1973), 317-320. MR 0313901 (47:2453)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10

Retrieve articles in all journals with MSC: 47H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0467416-7
Keywords: Fixed point, fixed point index, k-set-contraction, measure of noncompactness, $ \alpha $-Lipschitz operator, degree theory
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society