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Proceedings of the American Mathematical Society

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Remarks on fixed points and boundaries

Author: W. A. Kirk
Journal: Proc. Amer. Math. Soc. 87 (1983), 62-64
MSC: Primary 47H10
MathSciNet review: 677232
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Abstract: It is shown that three recent fixed point theorems of E. Chandler for nonexpansive mappings defined on compact subsets of strictly convex normed linear spaces hold in arbitrary normed linear spaces.

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

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  • [2] E. Chandler, Fixed points and boundaries, Proc. Amer. Math. Soc. 82 (1981), 398-400. MR 612728 (82j:47071)
  • [3] C. M. Dafermos and M. Slemrod, Asymptotic behavior of nonlinear contraction semigroups, J. Funct. Anal. 13 (1973), 97-106. MR 0346611 (49:11336)
  • [4] R. De Marr, Common fixed-points for commuting contraction mappings, Pacific J. Math. 13 (1963), 1139-1141. MR 0159229 (28:2446)
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  • [6] W. A. Kirk, Locally nonexpansive mappings in Banach spaces (Proc. Workshop Fixed Point Theory, Univ. de Sherbrooke, June 1980), Lecture Notes in Math., vol. 886, Springer-Verlag, Berlin and New York, 1981. MR 643007 (84g:47047)

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Keywords: Nonexpansive mappings, fixed points, normed linear spaces
Article copyright: © Copyright 1983 American Mathematical Society

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