Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 20962, 12 pages
doi:10.1155/2007/20962
Research Article

Fixed Points of Weakly Contractive Maps and Boundedness of Orbits

Jie-Hua Mai1 and Xin-He Liu2

 1Institute of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2Institute of Mathematics, Guangxi University, Nanning, Guangxi 530004, China
Received 10 October 2006; Revised 8 January 2007; Accepted 31 January 2007

Recommended by William Art Kirk

Abstract

We discuss weakly contractive maps on complete metric spaces. Following three methods of generalizing the Banach contraction principle, we obtain some fixed point theorems under some relatively weaker and more general contractive conditions.