Geodesic
Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces
Liu, Ying1
1 College of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 395-409.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.02.06
Classification : 47H09, 47H05, 47H06, 47J25, 47J05
Keywords: Subgradient extragradient method, Halpern method, generalized projection operator, monotone mapping, variational inequality, relatively nonexpansive mapping.

Liu, Ying 1

1 College of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, China 
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Liu, Ying. Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 395-409. doi : 10.22436/jnsa.010.02.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.06/

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