Parallel composite-type extragradient implicit method for a system of variational inclusions with the common fixed-point constraint of pseudocontractive mappings

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 -uniformly Lipschitzian pseudocontractive mappings.In this paper, we introduce a parallel composite-type extragradient implicit method for solving a general system of variational inclusions (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 appropriate assumptions.As applications, we apply our main result to the variational inequality problem (VIP), split feasibility problem (SFP) and LASSO problem in Hilbert spaces.