In this paper, we introduce a suitable Mann type algorithm for finding a common element of
the set of solutions of systems of equilibrium problems and the set of common fixed points
of an infinite family and left amenable semigroup of nonexpansive mappings in Hilbert
spaces. Then we prove the strong convergence of the proposed iterative scheme to the
unique solution of the minimization problem on the solution of systems of equilibrium
problems and the common fixed points of an infinite family and left amenable semigroup
of nonexpansive mappings. Our results extend and improve the recent result of Colao and
Marino [V. Colao and G. Marino, Strong convergence for a minimization problem on points
of equilibrium and common fixed points of an infinite family of nonexpansive mappings,
Nonlinear Anal. 73 (2010) 3513–3524] and many others.