ON THE CONVERGENCE OF AN ITERATION PROCESS FOR TOTALLY ASYMPTOTICALLY I-NONEXPANSIVE MAPPINGS

Abstract

Suppose that K be a nonempty closed convex subset of a real Banach space X and T,S:K???K be two totally asymptotically I-nonexpansive mappings, where I:K???K is a totally asymptotically nonexpansive mapping. We define the iterative sequence {x_{n}} by
{<K1.1/>,n??????,???
<K1.1 ilk="MATRIX" >x??????Kx_{n+1}=(1-??_{n})x_{n}+??_{n}S?เธขย?y_{n}y_{n}=(1-??_{n})x_{n}+??_{n}T?เธขย?z_{n}z_{n}=(1-??_{n})x_{n}+??_{n}I?เธขย?x_{n}</K1.1>where {??_{n}},{??_{n}} ve {??_{n}} are sequences in [0,1].Under some suitable conditions, the strong and weak convergence theorems of {x_{n}} to a common fixed point of S,T and I are obtained.