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Zbl 1147.65048
Qin, Xiaolong; Shang, Meijuan; Zhou, Haiyun
Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces. (English)
[J] Appl. Math. Comput. 200, No. 1, 242-253 (2008). ISSN 0096-3003

The authors introduce a new iterative method to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. No numerical tests are presented.
[Hans Benker (Merseburg)]

MSC 2000:: *65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities
65J15 Equations with nonlinear operators (numerical methods)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49M20 Methods of relaxation type

Keywords: projection method; relaxed cocoercive mapping; nonexpansive mapping; fixed point; convergence; Hilbert space

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Zentralblatt MATH Berlin [Germany]