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Fixed point theorems in uniformly rotund metric spaces

Published online by Cambridge University Press:  17 April 2009

John Staples
John Staples
Affiliation:
Department of Mathematics, Queensland Institutie of Technology, North Quay, Queensland.
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Abstract

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In recent years fixed point theorems have been proved for non-expansive and similar mappings on uniformly convex Banach spaces. The only role the linear structure plays in the statement of these results occurs in the definition of uniform convexity. It is therefore natural to ask whether the results depend essentially on the linear structure, or whether an extension of the notion of uniform convexity to metric spaces would allow the hypothesis of linear structure on the underlying space to be removed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 2 , April 1976 , pp. 181 - 192
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Cooper, T.J. and Michael, J.H., “Two fixed point theorems and invariant integrals”, Bull. Austral. Math. Soc. 11 (1974), 15–30.Google Scholar
[2]Edelstein, Michael, “The construction of an asymptotic centre with a fixed point property”, Bull. Amer. Math. Soc. 78 (1912), 206–208.Google Scholar
[3]Edelstein, Michael, “Fixed point theorems in uniformly convex Banach spaces”, Proc. Amer. Math. Soc. 44 (1971), 369–374.Google Scholar