International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 845-853
doi:10.1155/IJMMS.2005.845
Coincidence and common fixed point theorems in compact Hausdorff spaces
Zeqing Liu1
, Haiyan Gao1
, Shin Min Kang3
and Yong Soo Kim4
1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, China
3Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
4Department of Mathematics and Research Institute of Natural Science, Gyeongsang, National University, Chinju 660-701, Korea
Abstract
The existence of coincidence and fixed points for continuous mappings in compact Hausdorff spaces is established. Some equivalent conditions of the existence of fixed and common fixed points for any continuous mapping and a pair of mappings in compact Hausdorff spaces are given, respectively. Our results extend, improve, and unify the corresponding results due to Jungck, Liu, and Singh and Rao.