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 [1], Chang et al. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].
Keywords : $\phi $-pseudocontractive operator, $\phi $-hemicontractive operators, the three-step iteration method with errors, fixed point, Banach spaces
MSC numbers : 47H05, 47H06, 47H10, 47H14
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