Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces
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Authors
Ying Liu
- College of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, China.
Abstract
In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a
variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator
and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of
finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a relatively
nonexpansive mapping. Our results improve some well-known results in Banach spaces or Hilbert spaces.
Share and Cite
ISRP Style
Ying Liu, Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 395--409
AMA Style
Liu Ying, Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(2):395--409
Chicago/Turabian Style
Liu, Ying. "Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 395--409
Keywords
- Subgradient extragradient method
- Halpern method
- generalized projection operator
- monotone mapping
- variational inequality
- relatively nonexpansive mapping.
MSC
- 47H09
- 47H05
- 47H06
- 47J25
- 47J05
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