Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces
- College of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, China.
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.
- Subgradient extragradient method
- Halpern method
- generalized projection operator
- monotone mapping
- variational inequality
- relatively nonexpansive mapping.
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