Strong convergence theorems of the modified Reich-Takahashi iteration method in Banach spaces
Yong Ming Fu · Fuzhou daxue xuebao. Ziran kexue ban · 2009
Let E be a real p-uniformly smooth Banach space(1p≤2),D be a nonempty closed convex subset of E,which is also a nonexpansive retract of E.Let T ∶ D→E is a nonself asymptotically nonexpansive mapping with a sequence{kn}[1,∞),limn→∞kn=1,P ∶ E→D be a nonexpansive retraction.It is shown that under some suitable conditions,the sequence {xn} defined by the modifiedReich-Takahashi iteration method(1)and(2)converges strongly to the fixed point of nonself asymptotically nonexpansive mapping T.