WEAK AND STRONG CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS WITH TSENG'S EXTRAGRADIENT METHOD

The paper is concerned with the problem of finding a common solution of a variational inequality problem governed by Lipschitz continuous monotone mappings and of a fixed point problem of nonexpansive mappings. To solve this problem, we introduce two new iterative algorithms which are based on Tseng...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 16; no. 3; pp. 1125 - 1136
Main Authors Wang, Fenghui, Xu, Hong-Kun
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2012
Subjects
Applied mathematics
College mathematics
Hilbert spaces
Mathematical inequalities
Mathematical theorems
Perceptron convergence procedure
Variational inequalities
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Summary:The paper is concerned with the problem of finding a common solution of a variational inequality problem governed by Lipschitz continuous monotone mappings and of a fixed point problem of nonexpansive mappings. To solve this problem, we introduce two new iterative algorithms which are based on Tseng's extragradient method. Moreover we prove the weak and strong convergence of these new algorithms to a solution of the above-stated problem. 2010Mathematics Subject Classification: Primary 47J20, 49J40; Secondary 47H05, 47H10, 47H09. Key words and phrases: Lipschitz continuity, Nonexpansive mapping, Variational inequality problem, Iterative algorithms, Projection, Fixed point, Extragradient method.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406682