Convergence Theorems of CQ Iteration Processes for a Finite Family of Averaged Mappings in Hilbert Spaces 1
Jing Sun, Yanrong Yu, Rudong Chen · 2008
In this paper, we study convergence theorems of CQ iteration processes for averaged mappings in Hilbert spaces. Let K be a bounded closed convex subset of a real Hilbert space H and Let {Ti} N=1 : K → K be a finite family averaged mappings such that F = ∩ N=1 F(Ti) � ∅. Assume that {αn} is real number sequences in (0,1) such that limn→∞ αn = 0. Define a sequence {xn} ∞=1 in K by the algorithm: