Abstract and Applied Analysis
Volume 2010 (2010), Article ID 763207, 12 pages
doi:10.1155/2010/763207
Mixed approximation for nonexpansive mappings in Banach spaces
Qing-Bang Zhang1
, Fu-Quan Xia2
and Ming-Jie Liu1
1College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
2Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610064, China
Abstract
The mixed viscosity approximation is proposed for finding fixed points of nonexpansive mappings, and the strong convergence of the scheme to a fixed point of the nonexpansive mapping is proved in a real Banach space with uniformly Gâteaux differentiable norm. The theorem about Halpern type approximation for nonexpansive mappings is shown also. Our theorems extend and improve the correspondingly results shown recently.