Iterative Process for a Common Fixed Point of a Finite Family of Asymptotically k-Pseudocontractive Maps

Abstract

Let $K$ be a closed convex nonempty subset of a Hilbert space $H$ and let $\{T_i\}_{i=1}^N$ be a finite family of Asymptotically k-pseudocontractive maps from $K$ into itself with $F = ∩_{i=1}^NF(T_i) not empty. Sufficient conditions for the strong convergence of the sequence of successive approximations generated by a Picard-like process to a common fixed point of the family are proved.