No abstract

In this paper we study the approximation of common fixed points of a finite family of nonexpansive mappings in uniformly smooth Banach spaces. Also we show that the convergence of the proposed algorithm can be proved under some types of control conditions.

We introduce an iterative method for finding a common fixed point of a semigroup of infinite family of nonexpansive mappings in Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real valued functions of the semigroup. 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.