AN ITERATIVE METHOD FOR AMENABLE SEMIGROUP AND INFINITE FAMILY OF NON EXPANSIVE MAPPINGS IN HILBERT SPACES

We introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. The results presented here mainly extend the corresponding results announced by Qin et al. and several others.