On generalized extragradient implicit method for systems of variational inequalities with constraints of variational inclusion and fixed point problems
Lu-Chuan Ceng, Li-Jun Zhu, Tzu-Chien Yin · Open Mathematics · 2022
Abstract In a real Banach space, let the VI indicate a variational inclusion for two accretive operators and let the CFPP denote a common fixed point problem of countably many nonexpansive mappings. In this article, we introduce a generalized extragradient implicit method for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints. Strong convergence of the suggested method to a solution of the GSVI with the VI and CFPP constraints under some suitable assumptions is established.