Viscosity algorithm for solving split generalized equilibrium problem and fixed-point problem

This article considers a split generalized equilibrium problem and fixed point problem for infinite family of nonexpansive mapping in Hilbert space. We propose an algorithm for finding a common solution of these problems. Under mild assumptions, we establish a strong convergence theorem for the sequence generated by the proposed algorithm using viscosity technique. We present the implementation of the proposed algorithm by considering some numerical illustrations and comparison of the proposed algorithm with an existing algorithm in the literature.