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A CONVERGENCE THEOREM ON QUASI-ϕ-NONEXPANSIVE MAPPINGS  

Kang, Shin Min (Department of Mathematics and the RINS Gyeongsang National University)
Cho, Sun Young (Department of Mathematics Gyeongsang National University)
Kwun, Young Chel (Department of Mathematics Dong-A University)
Qin, Xiaolong (Department of Mathematics Gyeongsang National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.1, 2010 , pp. 73-82 More about this Journal
Abstract
In an infinite-dimensional Hilbert space, the normal Mann iteration has only weak convergence, in general, even for nonexpansive mappings. The purpose of this paper is to modify the normal Mann iteration to have strong convergence for a closed quasi-$\phi$-nonexpansive mapping in the framework of Banach spaces.
Keywords
strong convergence; hybrid algorithm; nonexpansive mapping; Banach space;
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