Strong Convergence Theorems for Nonself I-Asymptotically Quasi-Nonexpansive Mappings 1
Si-Sheng Yao, Lin Wang · 2008
Let X be a real uniformly convex Banach space, C be a nonempty closed convex subset of X. Let I : C → X be a nonself asymptotically nonexpansive mapping and T : C → X be a nonself I-asymptotically quasi-nonexpansive mapping. Let {xn} be a sequence generated by: for any given x1 ∈ C, yn = P(βnT( PT ) n−1 xn +( 1− βn)xn), xn+1 = P(αnI( PI ) n−1 yn +( 1− αn)xn), n ≥ 1, where {αn} and {βn} are two real sequences in [e,1 − e] for some e> 0. The strong convergnece theorems of {xn} to some x ∈ F(T) ∩ F(I) are proved under some appropriate conditions.