Fixed Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces
HU Chang-song · Mathematica Applicata · 2004
Let X be a uniformly convex Banach space,and let D be a nonempty closed,bounded,and convex subset of X,let T be a completely continuous asymptotically nonexpansive self-map of D with {k n} satisfying k n≥1,∑∞ n=1(k n-1)∞ and F(T)≠.Let {x n},{y n},{z n} be the sequence generated by definition 2 and ∑∞ n=1c n∞,∑∞ n=1c′ n∞,∑∞ n=1c″ n∞ and (i) b″ n∈[a,b](0,1);b′ n∈[0,β];b n∈[0,α],αβ+β1 or (ii) b′ n∈[a,b](0,1);b″ n∈[a,1];b n∈[0,b] or (iii) b n∈[a,b](0,1);b′ n∈[a,1],then {x n},{y n},{z n} converges strongly to some fixed point of T.