Taiwanese Journal of Mathematics


Yonghong Yao, Yeong-Cheng Liou, and Chia-Ping Chen

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In this paper, we construct two algorithms for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an $\alpha$-inverse-strongly monotone mapping in a Hilbert space. We show that the sequence converges strongly to a common element of two sets under the some mild conditions on parameters. As special cases of the above two algorithms, we obtain two schemes which both converge strongly to the minimum norm element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an $\alpha$-inverse-strongly monotone mapping.

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Taiwanese J. Math., Volume 15, Number 5 (2011), 1979-1998.

First available in Project Euclid: 18 July 2017

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Primary: 47H05: Monotone operators and generalizations 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47J25: Iterative procedures [See also 65J15]

metric projection inverse-strongly monotone mapping nonexpansive mapping variational inequality minimum-norm


Yao, Yonghong; Liou, Yeong-Cheng; Chen, Chia-Ping. ALGORITHMS CONSTRUCTION FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS. Taiwanese J. Math. 15 (2011), no. 5, 1979--1998. doi:10.11650/twjm/1500406418. https://projecteuclid.org/euclid.twjm/1500406418

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