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BanachJ.Math.Anal.2(2008),no.1,1–10 STRONGCONVERGENCEOFMONOTONECQALGORITHMFORRELATIVELYNONEXPANSIVEMAPPINGS B J M A

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Banach J. Math. Anal. 2 (2008), no. 1, 1–10

B

anach

J

ournal of

M

athematical

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nalysis ISSN: 1735-8787 (electronic)

http://www.math-analysis.org

STRONG CONVERGENCE OF MONOTONE CQ ALGORITHM FOR RELATIVELY NONEXPANSIVE MAPPINGS

YONGFU SU1,∗, MEIJUAN SHANG2, DONGXING WANG3 Submitted by M. S. Moslehian

Abstract. X. Qin and Y. Su proved a strong convergence theorems of mod- ified Ishikawa iteration by CQ method for relatively nonexpansive mappings in a Banach space [Xiaolong Qin, Yongfu Su, Nonlinear Anal. 67 (2007), no.

6, 1958–1965]. The result of this paper extends and improves the result of X.

Qin and Y. Su in the two respects: (1). By using the monotone CQ method to modify the CQ method, so that the new method of proof is used. (2). Relax the restriction on T from uniformly continuous to continuous. The result of this paper also extends and improves the recent ones announced by Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others.

1,3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China.

E-mail address: 1[email protected], 3[email protected]

2 Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China.

E-mail address: [email protected]

Date: Received: 28 May 2007; Accepted: 17 August 2007.

∗ Corresponding author.

2000Mathematics Subject Classification. Primary 47H05; Secondary 47H09, 47H10.

Key words and phrases. Relatively nonexpansive mapping, generalized projection, asymp- totic fixed point, monotone CQ method.

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