Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 734181, 21 pages
doi:10.1155/2010/734181
Robustness of Mann type algorithm with perturbed mapping for nonexpansive mappings in Banach spaces
L.C. Ceng1
, Y.C. Liou2
and J.C. Yao3
1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Information Management, Cheng Shiu University, no.840, Chengcing Road, Niaosong Township, Kaohsiung County 833, Taiwan
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
Abstract
The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)−λnμnF(xn) remains convergent in a Banach space setting where λn,μn∈[0,1], T a nonexpansive mapping, en, n=0,1,…, errors and F a strongly accretive and strictly pseudocontractive mapping.