Convergence Theorem of Modified IshikawaIterative Sequences for Asymptotically Nonexpansive Mappings
Xiaoping Xu · Journal of Huaiyin Teachers College · 2010
Let C be a nonempty bounded closed convex subset of uniformly convex Banach space.Let T:C→C be an asymptotically nonexpansive mapping.It is shown that under some suitable conditions such as thatE* satisfies KKproperty,Thas fixed point if and only if the modifiedIshikawaiterative sequences {xn}defined by xn+1=tnTnyn+(1-tn)xn yn=snTnxn+(1-sn)xn converges weakly and xn-Txn→0.