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Zbl 1189.47068
Qin, Xiaolong; Cho, Sun Young; Kang, Shin Min
(Qin, Xiao-long)
Strong convergence of shrinking projection methods for quasi-nonexpansive mappings and equilibrium problems. (English)
[J] J. Comput. Appl. Math. 234, No. 3, 750-760 (2010). ISSN 0377-0427

Summary: The purpose of this paper is to consider the convergence of a shrinking projection method for a finite family of quasi-$\phi$-nonexpansive mappings and an equilibrium problem. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties

Keywords: quasi-$\phi$-nonexpansive mapping; relatively nonexpansive mapping; generalized projection; equilibrium problem

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