Taiwanese Journal of Mathematics

ALGORITHMS CONSTRUCTION FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS

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

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406418

Digital Object Identifier
doi:10.11650/twjm/1500406418

Mathematical Reviews number (MathSciNet)
MR2880388

Zentralblatt MATH identifier
05990168

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

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

Citation

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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