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Zbl 1218.47101
Hu, Lianggen; Liu, Liwei
(Hu, Liang-gen; Liu, Li-wei)
A new iterative algorithm for common solutions of a finite family of accretive operators. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 6, A, 2344-2351 (2009). ISSN 0362-546X

Summary: The purpose in this paper is to prove strong convergence to a common solution for a finite family of accretive operators in a strictly convex Banach space by means of a new iterative algorithm, thus generalizing and extending the results of [{\it T.-H. Kim} and {\it H.-K. Xu}, Nonlinear Anal., Theory Methods Appl. 61, No.~1--2, A, 51--60 (2005; Zbl 1091.47055)] and [{\it H. Zegeye} and {\it N. Shahzad}, ibid. 66, No.~5, A, 1161--1169 (2007; Zbl 1120.47061)]. Furthermore, strong convergence to a common fixed point is discussed for a finite family of pseudocontractive mappings under certain conditions.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H06 Accretive operators, etc. (nonlinear)
47H09 Mappings defined by "shrinking" properties

Keywords: accretive operator; resolvent; pseudocontractive mappings; uniformly Gâteaux differentiable norm; common zeros; strong convergence

Citations: Zbl 1091.47055; Zbl 1120.47061

Cited in: Zbl 1213.65079

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