Iterative Approximation with Errors of a Finite Family of Non-self Nonexpansive Mappings in Banach Spaces
Zhao Liang-cai · Journal of Sichuan Normal University · 2008
Let E be a real uniformly convex Banach space and K a nonempty closed convex subset of E which is also a nonexpansive retract of E.Let T1,T2,…,TN:K → E be N nonexpansive mappings.It is shown that under some suitable conditions,the iterative sequence with errors {xn} defined byxn+1=P[(1-an1)xn+an1T1yn1+un1],yn1=P[(1-an2)xn+an2T2yn2+un2],……ynN-2=P[(1-anN-1)xn+anN-1TN-1ynN-1+unN-1],ynN-1=P[(1-anN)xn+anNTNxn+unN],n≥1converges weakly and strongly to some common fixed point.The results presented in this paper also extend and improve some known recent results.