A FIXED POINT THEOREM REVISITED

  • Kirk, W.A. (Department of Mathematics The University of Iowa) ;
  • Kang, B.G. (Department of Mathematics Sungshin Womens University )
  • Published : 1997.05.01

Abstract

In this paper, we obtain an abstract formulation of a fixed point theorem for nonexpansive mappings. Our theorem is a non-metric version of Kirk's original theorem.

Keywords

References

  1. Nonstandard Methods in Fixed Point Theory A. G. Aksoy;M. A. Khamsi
  2. Proc. Amer. Math. Soc. v.82 A fixed point free nonexpansive map D. E. Alspach
  3. Theory and Applications of Distance Geometry L. M. Blumenthal
  4. Dokl. Akad. Nauk SSSR v.59 On the center of a convex set (Russian) M. S. Brodskii;D. P. Milman
  5. Proc. Nat. Acad. Sci. U.S.A. v.54 Nonexpansive nonlinear operators in a Banach space F. E. Browder
  6. Constructive aspects of fixed point theory for nonexpansive mappings T. Buber;W. A. Kirk
  7. J. London Math. Soc. v.37 On fixed and periodic points under contractive mappings M. Edelstein
  8. Topics in Metric Fixed Point Theory K. Goebel;W. A. Kirk
  9. Math. Nachr. v.30 Zum Prinzip der kontraktiven Abbildungen D. G ohde
  10. Amer. Math. Monthly v.72 A fixed point theorem for mappings which do not increase distances W. A. Kirk
  11. Rend. Sem. Mat. e Fis. di Milano v.LI Nonexpansive mappings in metric and Banach spaces W. A. Kirk
  12. Bull. Math. Soc. France, Memoire v.60 Fixed point theorems without convexity J. P. Penot
  13. General Topology S. Willard