Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 16, Number 3 (2012), 1125-1136.
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's extragradient method. Moreover we prove the weak and strong convergence of these new algorithms to a solution of the above-stated problem.
Taiwanese J. Math., Volume 16, Number 3 (2012), 1125-1136.
First available in Project Euclid: 18 July 2017
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 49J40: Variational methods including variational inequalities [See also 47J20]
Secondary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
Wang, Fenghui; Xu, Hong-Kun. WEAK AND STRONG CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS WITH TSENG’S EXTRAGRADIENT METHOD. Taiwanese J. Math. 16 (2012), no. 3, 1125--1136. doi:10.11650/twjm/1500406682. https://projecteuclid.org/euclid.twjm/1500406682