ON PARALLEL MANN-TYPE EXTRAGRADIENT ALGORITHMS FOR SYSTEMS OF VARIATIONAL INEQUALITIES WITH CONSTRAINTS OF VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS

In a uniformly convex and q-uniformly smooth Banach space with q ∈ (1,2], let the VI indicate a variational inclusion for two accretive operators and let the CFPP denote a common fixed point problem of a countable family of nonexpansive mappings. In this paper, we introduce a parallel Mann type extragradient algorithm for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints. We then prove the strong convergence of the suggested algorithm to a solution of the GSVI with the VI and CFPP constraints under some suitable assumptions. As applications, we apply our main result to the variational inequality problem (VIP), split feasibility problem (SFP) and LASSO problem in Hilbert spaces.