Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings

被引：37

作者：

Yao Y. ^{[1
]}

Zhou H. ^{[2
]}

Liou Y.-C. ^{[3
]}

机构：

[1] Department of Mathematics, Tianjin Polytechnic University

[2] Department of Mathematics, Shijiazhuang Mechanical Engineering College

[3] Department of Information Management, Cheng Shiu University

来源：

Journal of Applied Mathematics and Computing | 2009年 / 29卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Fixed point; Krasnoselski-Mann iterative algorithm; Non-expansive mapping; Strong convergence;

D O I：

10.1007/s12190-008-0139-z

中图分类号：

学科分类号：

摘要：

In this paper, we introduce a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings. Furthermore, we prove that the proposed iterative algorithm converges strongly to a fixed point of a non-expansive mapping in Hilbert spaces.

引用

页码：383 / 389

页数：6

共 15 条

[1]

Browder F.E., Petryshyn W.V., Construction of fixed points of nonlinear mappings, J. Math. Anal. Appl., 20, pp. 197-228, (1967)

[2]

Byrne C., A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl., 20, pp. 103-120, (2004)

[3]

Podilchuk C.I., Mammone R.J., Image recovery by convex projections using a least-squares constraint, J. Opt. Soc. Am., 7, pp. 517-521, (1990)

[4]

Reich S., Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67, pp. 274-276, (1979)

[5]

Genel A., Lindenstrass J., An example concerning fixed points, Isr. J. Math., 22, pp. 81-86, (1975)

[6]

Xu H.K., Iterative algorithms for nonlinear operators, J. Lond. Math. Soc., 2, pp. 240-256, (2002)

[7]

Borwein J., Reich S., Shafrir I., Krasnoselski-Mann iterations in normed spaces, Can. Math. Bull., 35, pp. 21-28, (1992)

[8]

Eckstein J., Bertsekas D.P., On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program., 55, pp. 293-318, (1992)

[9]

Yang Q., Zhao J., Generalized KM theorems and their applications, Inverse Probl., 21, pp. 1971-1979, (2006)

[10]

Zhao J., Yang Q., A note on the Krasnoselski-Mann theorem and its generalizations, Inverse Probl., 23, pp. 1011-1016, (2007)

← 1 2 →