STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES* |
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Authors: | Yongfu Su Xiaolong Qin |
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Institution: | (1) Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China |
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Abstract: | K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonexpansive mappings, nonexpansive semigroups,
and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical
programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the
monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone
hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs
in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial’s condition.
*This research is supported by the National Natural Science Foundation of China under Grant No. 10771050. |
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Keywords: | Hybrid method nonexpansive mapping nonexpansive semigroup proximal point algorithm strong convergence |
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