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Zbl 1199.47295
Su, Yongfu; Gao, Junyu; Zhou, Haiyun
(Su, Yong-fu; Gao, Jun-yu; Zhou, Hai-yun)
Monotone $CQ$ algorithm of fixed points for weak relatively nonexpansive mappings and applications. (English)
[J] J. Math. Res. Expo. 28, No. 4, 957-967 (2008). ISSN 1000-341X

Summary: {\it S.-Y.\thinspace Matsushita} and {\it W.\, Takahashi} [J.~Approx.\ Theory 134, No.\,2, 257--266 (2005; Zbl 1071.47063)] proved a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method ($CQ$ method) in mathematical programming. The purpose of this paper is to modify this method and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of our monotone CQ method is faster than the hybrid method of [op.\,cit.]. In addition, the Cauchy sequence method is used in this paper without using the Kadec-Klee property.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
65J15 Equations with nonlinear operators (numerical methods)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H05 Monotone operators (with respect to duality)

Keywords: weak relatively nonexpansive mapping; asymptotic fixed point; maximal monotone operator

Citations: Zbl 1071.47063

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