An approximation method for continuous pseudocontractive mappings
Yisheng Song, Rudong Chen · Journal of Inequalities and Applications · 2006
Let be a closed convex subset of a real Banach space , is continuous pseudocontractive mapping, and is a fixed -Lipschitzian strongly pseudocontractive mapping. For any , let be the unique fixed point of . We prove that if has a fixed point and has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then converges to a fixed point of as approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).