Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces

The purpose of this paper is to study the convergence problem of the iteration scheme xn+1 = λn+1y +(1–λn+1) Tn+1xn for a family of infinitely many nonexpansive mappings T1, T2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.