Weak and strong convergence of Krasnoselski–Mann iteration for hierarchical fixed point problems
Yonghong Yao, Yeong‐Cheng Liou · Inverse Problems · 2008
This paper deals with a method for approximating a solution of the following fixed point problem: find ; , where H is a Hilbert space, P and T are two nonexpansive mappings on a closed convex subset C and proj Fix( T ) denotes the metric projection on the set of fixed points of T . First, we prove a weak convergence theorem which extends and improves a recent result announced by Moudafi (2007 Inverse Problems 23 1635–40). Secondly, when P is a contraction, a special case of nonexpansive mappings, we prove a strong convergence result under different restrictions on parameters for solving the above fixed point problem.