Parallel extragradient-type viscosity algorithm for a variational inclusion and a system of variational inclusions with countable nonexpansive mappings

In a Banach space that is uniformly convex and q-uniformly smooth with q in the range (1, 2], consider VI as representing a variational inclusion involving two accretive operators, and CFPP as denoting a common fixed point problem for a countable set of nonexpansive mappings.This paper presents a parallel extragradient-type viscosity algorithm designed to address a general system of variational inclusions (GSVI) constrained by VI and CFPP.We establish the strong convergence of the proposed algorithm to a solution of the GSVI under the VI and CFPP constraints, assuming certain mild conditions.As practical applications, we extend our main results to the variational inequality problem (VIP), the split feasibility problem (SFP), and the LASSO problem within Hilbert spaces.