Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 714860, 19 pages
Research Article

On the Convergence of an Implicit Iterative Process for Generalized Asymptotically Quasi-Nonexpansive Mappings

1School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
4Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 27 June 2010; Revised 16 October 2010; Accepted 10 November 2010

Academic Editor: Naseer Shahzad

Copyright © 2010 Xiaolong Qin 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.


The purpose of this paper is to introduce and consider a general implicit iterative process which includes Schu's explicit iterative processes and Sun's implicit iterative processes as special cases for a finite family of generalized asymptotically quasi-nonexpansive mappings. Strong convergence of the purposed iterative process is obtained in the framework of real Banach spaces.