| Monotone CQ Algorithm of Fixed Points for Weak Relatively Nonexpansive Mappings and Applications |
| Received:September 22, 2006 Revised:March 23, 2007 |
| Key Words:
weak relatively nonexpansive mapping generalized projection asymptotic fixed point monotone $CQ$ method maximal monotone operator.
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| Fund Project:the National Natural Science Foundation of China (No.10771050). |
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| Abstract: |
| Matsushita, Takahashi$^{[4]}$ proved a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method ($CQ$ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Takahashi by monotone $CQ$ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone $CQ$ method is faster than the hybrid method of Matsushita, Takahashi. In addition, the Cauchy sequence method is used in this paper without using the Kadec-Klee property. The results of this paper modify and improve the results of Matsushita, Takahashi and some others. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.028 |
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