Viscosity approximation method for accretive operator in Banach space
- 作者：Rudong Chen ; Zhichuan Zhu
- 关键词：Accretive operator ; Uniformly smooth ; Fixed point ; Banach limit
- 刊名：Nonlinear Analysis
- 出版年：2008
- 期刊代码：43_0362546x
- 类别：mt
- 出版时间：15 August 2008
- 卷：69
- 期：4
- 页码：1356-1363
- 文件大小：214 K
摘要
Let X be a uniformly smooth Banach space, 53caf050bb80ce3432102" title="Click to view the MathML source" alt="Click to view the MathML source">C be a closed convex subset of X, and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm
where
n and γn are two sequences satisfying certain conditions, Jr denotes the resolvent (I+rA)−1 for r>0, and f:C→C be a fixed contractive mapping. Then as c352a8817e3b4" title="Click to view the MathML source" alt="Click to view the MathML source">n→∞, the sequence {xn} strongly converges to a point in F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu [Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643].
where
n and γn are two sequences satisfying certain conditions, Jr denotes the resolvent (I+rA)−1 for r>0, and f:C→C be a fixed contractive mapping. Then as c352a8817e3b4" title="Click to view the MathML source" alt="Click to view the MathML source">n→∞, the sequence {xn} strongly converges to a point in F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu [Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643].