Ishikawa's iterative algorithm of nonexpansive mappings and averaged mappings

Abstract

In this paper we introduce and study Ishikawa's iterative algorithm of nonexpansive mapping and averaged mappings in the setting of real Hilbert spaces. The main results presented in this paper extend the classic result of convergence of Mann's iterative algorithm for nonexpansive mappings in the setting of Hilbert space and we prove the weak converge theorems. © 2013 Springer-Verlag.