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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 15, Pages 763-775
http://dx.doi.org/10.1155/S0161171204309269

Convergence theorems for uniformly quasi-Lipschitzian mappings

1Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
2Department of Mathematics, Research Institute of Natural Sciences, College of Natural Sciences, Gyeongsang National University, Chinju 660-701, South Korea
3Department of Mathematics, Education Research Institute of Natural Sciences, College of Education, Gyeongsang National University, Chinju 660-701, South Korea

Received 15 September 2003

Copyright © 2004 Hindawi Publishing Corporation. 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

We prove some convergence theorems of the modified Ishikawa iterative sequence with errors for uniformly quasi-Lipschitzian mappings in metric spaces. Our results generalize and improve the corresponding results of Petryshyn and Williamson, Ghosh and Debnath, Liu, and many others.