Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings

Let CC be a nonempty, closed and convex subset of a real Hilbert space HH. Let Ti:C→H,i=1,2,…,N, be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann’s type method to a common fixed point of {Ti:i=1,2,…,N}{Ti:i=1,2,…,N} provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on TT or on CC. As a consequence, it is proved that Mann’s method converges for a fixed point of nonexpansive mapping provided that interior of F(T)≠0̸F(T)≠0̸. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.