International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 3, Pages 183-188
doi:10.1155/S0161171202204093

Fixed point theorems for densifying mappings and compact mappings

Zeqing Liu,1 Li Wang,1 Shin Min Kang,2 and Yong Soo Kim2

1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Liaoning, Dalian 116029, China
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

Received 8 April 2002

Copyright © 2002 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.

Abstract

The purpose of this note is to establish fixed point theorems for densifying mappings and compact mappings which are contractive in metric spaces and to investigate the existence of fixed points for a family of mappings in bounded metric spaces. The results of this note generalize the results of Bailey (1966) and Liu (1994).