TY - JOUR AU - Liu, Ying PY - 2017 TI - Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Banach spaces JO - Journal of Nonlinear Sciences and Applications SP - 395--409 VL - 10 IS - 2 AB - 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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