Convergence theorems of a three-step iteration method for a countable family of pseudocontractive mappings

The purpose of this paper is to construct a three-step iteration method (as follows) and obtain the convergence theorem for a countable family of Lipschitz pseudocontractive mappings in Hilbert space H. For the iteration format, {z(n) = (1 - gamma(n))x(n) + gamma(n)T(n)x(n), y(n) = (1 - beta(n))x(n) + beta(n)T(n)z(n), x(n+1) = (1 - alpha(n))x(n) + alpha(n)T(n)y(n), under suitable conditions, we prove that the sequence {x(n)} generated from above converges strongly to a common fixed point of {T-n}(n >= 1). The results obtained in this paper improve and extend previous results that have been proved for this class of nonlinear mappings.