Strong Convergence Theorems forα-nonexpansive Mapping in Uniformly Convex Banach Spaces
Ju Tan · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2015
Let Cbe a nonempty closed convex subset of a uniformly convex Banach space,and let T:C→Cbe a semi-compactα-nonexpansive mapping with fixed points,whereα1.For given x0≥C,suppose that the sequence{xn}is the Ishikawa iterative sequence with errors defined by xn+1=(1-αn-βn)xn+αnTyn+βnun,yn=(1-γn-δn)xn+γnTxn+δnvn,n=0,1,2,…,where 0A≤αn≤B1/2,0≤γn≤γ1,n=0,1,2,…,∞∑n=0βn∞,∞∑n=0δn∞,{un }and {vn}are two bounded sequences in C.It is proved that the sequence{xn}strongly converges to a fixed point of T.