A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings

Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly pseudo-contractive mappings which solves the variational inequality 〈(γf−μF)q,p−q〉≤0 for p∈⋂i=1∞F(Ti). Furthermore, we also prove the strong convergence theorems for the proposed iterative scheme and give a numerical example to support and illustrate our main theorem.