Strong convergence of Mann's type iteration method for an infinite family of generalized asymptotically nonexpansive nonself mappings in Hilbert spaces

Let be a nonempty closed convex subset of a real Hilbert space . Let be an infinite family of generalized asymptotically nonexpansive nonself mappings. By using a specific way of choosing the indexes of the involved mappings, we prove strong convergence of Mann's type iteration to a common fixed point of without the compactness assumption imposed either on or on provided that the interior of common fixed points is nonempty. The results extend previous results restricted to the situation of at most finite families of such mappings.