Acta Mathematica Sinica

, Volume 18, Issue 2, pp 363–374

On a Fixed Point Theorem of Ky Fan


DOI: 10.1007/s101140200165

Cite this article as:
De Blasi, F.S. & Georgiev, P.G. Acta Math Sinica (2002) 18: 363. doi:10.1007/s101140200165


We generalize a theorem of Ky Fan about the nearest distance between a closed convex set D in a Banach space E and its image by a function ƒ:DE, in several directions: (1) for noncompact sets D, when ƒ(D) precompact; (2) for compact D and upper semicontinuous multifunction ƒ and more generally, (3) for noncompact D and upper semicontinuous multifunction ƒ with ƒ(D) Hausdorff precompact.

In particular, we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions whose values are convex closed bounded, thus not necessarily compact.


Ky Fan, Compact hcompact Upper semicontinuous multifunction 

MR (2000) Subject Classification

47H10 54H25 

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Roma II 'Tor Vergata'RomaItaly
  2. 2.Department of Mathematics and InformaticsSofia University "St. Kl. Ohridski"SofiaBulgaria
  3. 3.Laboratory for Advanced Brain Signal Processing, Brain Science Institute, The Institute of Physical and Chemical Resarch (RIKEN) 2-1, Hirosawa, Wako-shiSaitamaJapan

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