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Strong convergence of shrinking projection methods for quasi--nonexpansive mappings and equilibrium problems

✍ Scribed by Xiaolong Qin; Sun Young Cho; Shin Min Kang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
328 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

The purpose of this paper is to consider the convergence of a shrinking projection method for a finite family of quasi-Ο†-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.

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The authors regret that the above-referenced paper contains a number of misprints. In the statement of Theorem 3.1 (Eq. (3.1)) the condition C n+1 is incorrect. In fact, the set C n+1 in Theorem 3.1 should be replaced by the following one: The proof on page 15 line 5 should be inserted with the fol