APPROXIMATING SOLUTION OF SYSTEM OF VARIATIONAL INEQUALITY CONSTRAINED SPLIT COMMON FIXED POINT PROBLEM IN HILBERT SPACES

We present a new modified viscosity technique in this article for solving the solution of the system of variational inequality problem, as well as the fixed point of single-valued ρ-strictly pseudocontractive mappings and finite families of multi-valued quasi-nonexpansive mappings within real Hilbert spaces. Using our iterative method, we establish a strong convergence result for approximating the solution of the aforementioned problems without any strict condition being imposed. We present some consequences and applications to validate our main result. Our result complements and generalizes some related results in literature.