International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 13-16, Pages 763-775
doi:10.1155/S0161171204309269
Convergence theorems for uniformly quasi-Lipschitzian mappings
Haiyun Zhou1
, Jung Im Kang2
, Shin Min Kang2
and Yeol Je Cho4
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
4Department of Mathematics, Education Research Institute of Natural Sciences, College of Education, Gyeongsang National University, Chinju 660-701, South Korea
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.