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A fixed point theorem for a class of star-shaped sets inc 0

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Abstract

A subsetK ofc 0 is coordinatewise star-shaped (c.s.s.) if there exists a center pointx ∈K such that fory ∈K andz ∈c 0, ifz is coordinatewise betweenx andy thenz ∈K. We prove that a weakly compact c.s.s. subset ofc 0 has the fixed point property for nonexpansive mappings and that a fixed point for such a mapping can be obtained in a constructive manner.

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References

  1. D. E. Alspach,A fixed point free nonexpansive map, preprint.

  2. D. G. de Figueiredo and L. Karlovitz,On the extension of contractions on normed spaces, inNonlinear Functional Analysis, Proc. Symp. Pure Math., Vol XVIII, Part 1, 1968, pp. 95–104.

  3. E. Odell and Y. Sternfeld,A fixed point theorem in c 0, to appear.

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Authors and Affiliations

  1. Oxford University, Oxford, England

    R. Haydon, E. Odell & Y. Sternfeld

  2. The University of Texas at Austin, Austin, Texas, USA

    R. Haydon, E. Odell & Y. Sternfeld

  3. Haifa University, Mt. Carmel, Israel

    R. Haydon, E. Odell & Y. Sternfeld

Authors
  1. R. Haydon
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  2. E. Odell
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  3. Y. Sternfeld
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Additional information

Research of the first two authors was partially supported by NSF Grant MCS78-01344 and of the last author by MCS78-01501.

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Haydon, R., Odell, E. & Sternfeld, Y. A fixed point theorem for a class of star-shaped sets inc 0 . Israel J. Math. 38, 75–81 (1981). https://doi.org/10.1007/BF02761850

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  • DOI: https://doi.org/10.1007/BF02761850

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