International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 7, Pages 391-397

On characterizations of fixed points

Zeqing Liu,1 Lili Zhang,1 and Shin Min Kang2

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

Received 16 January 2001; Revised 14 March 2001

Copyright © 2001 Zeqing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give some necessary and sufficient conditions for the existence of fixed points of a family of self mappings of a metric space and we establish an equivalent condition for the existence of fixed points of a continuous compact mapping of a metric space.