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Uniformly Lipschitzian Semigroups in Hilbert Space

Published online by Cambridge University Press:  20 November 2018

David J. Downing  and
William O. Ray
David J. Downing
Affiliation:
Department of Mathematical Sciences Oakland University, Rochester, Michigan48063
William O. Ray
Affiliation:
Department of Mathematics the University of Oklahoma, Norman, Oklahoma73019
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Abstract

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Let K be a closed, bounded, convex, nonempty subset of a Hilbert Space . It is shown that if is a left reversible, uniformly k-lipschitzian semigroup of mappings of K into itself, with k < √2, then has a common fixed point in K.

Keywords

47H10common fixed pointsuniformly k-lipschitzian semigroups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 210 - 214
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Goebel, K. and Kirk, W. A., A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math., 47 (1973), 135-140.Google Scholar
2. Goebel, K., Kirk, W. A., and Thele, R. L., Uniformly lipschitzian families of transformations in Banach spaces, Can. J. Math., 26 (1974), 1245-1256.Google Scholar
3. Holmes, R. B., A Course on Optimization and Best Approximation, Lecture Notes No. 257, Springer-Verlag, Berlin, Heidelberg, New York, 1972.Google Scholar
4. Lifschitz, E. A., Fixed point theorems for operators in strongly convex spaces, Voronež Gos. Univ. Trudy Math. Fak., 16 (1975), 23-28. (Russian)Google Scholar
5. Routledge, N., A result in Hilbert space, Quarterly J. Math., 3 (1952), 12-18.Google Scholar
6. Martin, R. H. Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley-Interscience, New York, London, Sydney, Toronto, 1976.Google Scholar