Iterative approximation of fixed points for $\phi$-hemicontractive
Commun. Korean Math. Soc. 2004 Vol. 19, No. 1, 63-74 Printed March 1, 2004
Zeqing Liu, Zhefu An, Yanjuan Li, Shin Min Kang Liaoning Normal University, Liaoning Normal University, Shenyang University, Gyeongsang National University
Abstract : Suppose that $X$ is a real Banach space, $K$ is a non\-em\-pty closed convex subset of $X$ and $T:K\to K$ is a uniformly continuous $\phi$-hemicontractive operator or a Lipschitz $\phi $-hemicontractive operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of $T$. Our results extend the corresponding results of Chang , Chang et al. , Chidume -, Chidume and Osilike , Deng , Liu and Kang , , Osilike ,  and Tan and Xu .
Keywords : $\phi $-pseudocontractive operator, $\phi $-hemicontractive operators, the three-step iteration method with errors, fixed point, Banach spaces