A modified hybrid method for solving variational inequality problems in Banach spaces
Journal of Nonlinear Functional Analysis · 2017
In this paper, we propose a hybrid type algorithm without the extrapolation step for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces.Based on the generalized projection operator and the Lyapunov functional introduced by Alber, we obtain the strong convergence of the iterative sequence generated in the hybrid algorithm.Our results extend and improve the corresponding results in [Y.V. Malitsky, V.V. Semenov, A hybrid method without extrapolation step for solving variational inequality problems, J. Global Optim.61 (2015), 193-202] and [K.Nakajo, Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces, Appl.Math.Comput.271 (2015), 251-258].