In this paper, we developed a viscosity-based extragradient iterative algorithm to approximate the solution of the split generalized equilibrium problem, the variational inequality problem, and the fixed point problem for a finite family of $ϵ$-strict pseudo-contractive and a nonexpansive mapping in Hilbert space. The main purpose was to establish strong convergence of the proposed algorithm under suitable conditions. We presented a comprehensive computational analysis to illustrate the effectiveness of our method and compared its performance with existing approaches. Our results extend and unify several well-known results in the literature, contributing significantly to the field.