On the closedness of sets with the fixed point property for contractions

Authors

  • Mira-Cristiana Anisiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy
  • Valeriu Anisiu "Babeş Bolyai" University, Cluj-Napoca, Romania

Keywords:

fixed point property, complete metric spaces, Banach spaces

Abstract

It is proved by examples that there exist (connected) non-closed sets with the fixed point property for contractions in complete metric spaces. In a Banach space, a convex set with nonvoid interior having the fixed point property for contractions is necessarily closed.

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References

E. H. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc. 10 (1959), pp. 974-979.

T. K. Hu, On afixed point theorem for metric spaces, Amer. Math. Monthly 74 (1967), 436-437.

P. V. Subrahmanyan, Completeness and fixed points, Monatsch. für Math. 80 (1975), pp. 325-330.

I. A. Rus, Maximal Fixed Point Structures, "Zilele academice clujene", 18-23 Nov. 1996.

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Published

1997-08-01

How to Cite

Anisiu, M.-C., & Anisiu, V. (1997). On the closedness of sets with the fixed point property for contractions. Rev. Anal. Numér. Théor. Approx., 26(1), 13–17. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1997-vol26-nos1-2-art2

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