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.
Qing-Bang Zhang. Fu-Quan Xia. Ming-Jie Liu. "Mixed Approximation for Nonexpansive Mappings in Banach Spaces." Abstr. Appl. Anal. 2010 1 - 12, 2010. https://doi.org/10.1155/2010/763207