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Zbl 1169.47056
Su, Yongfu; Shang, Meijuan; Wang, Dongxing
(Su, Yong-fu; Shang, Mei-juan; Wang, Dong-xing)
Strong convergence of monotone CQ algorithm for relatively nonexpansive mappings.
(English)
[J] Banach J. Math. Anal. 2, No. 1, 1-10, electronic only (2008). ISSN 1735-8787/e

This paper extends and improves the results of {\it X.--L.\thinspace Qin} and {\it Y.--F.\thinspace Su} [Nonlinear Anal., Theory Methods Appl.\ 67, No.\,6 (A), 1958--1965 (2007; Zbl 1124.47046)]. The extension and improvement are in two notable directions. (i) The authors employ the monotone CQ method to modify the CQ method of Qin and Su. (ii) The authors relax the restriction on $T: C \to C$ from uniformly continuous to continuous. Their monotone CQ method does not require the Kadec--Klee property, the demiclosedness principle, Opial's condition, or other weak topological technologies.
[Edward Prempeh (Kumasi)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H05 Monotone operators (with respect to duality)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: uniformly convex and uniformly smooth Banach spaces; relatively nonexpansive mapping; generalized projection; asymptotic fixed point; modified Ishikawa iteration; monotone CQ method

Citations: Zbl 1124.47046

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