Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces


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.


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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


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