Abstract and Applied Analysis
Volume 2013 (2013), Article ID 214230, 12 pages
Research Article

New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan

Received 24 September 2012; Revised 31 December 2012; Accepted 31 December 2012

Academic Editor: Naseer Shahzad

Copyright © 2013 Wei-Shih Du. 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.


Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are also presented.