Approximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces

This paper introduces an implicit scheme for a contin- uous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a sequence of invariant means de ned on an appropriate space of bounded, continuous real valued functions of the semigroup. The main result is to prove the strong convergence of the proposed implicit scheme to the unique solution of the variational inequality on the solution of systems of equilibrium problems and the common xed points of a sequence of nonexpansive mappings and a continuous representation of nonex- pansive mappings.