Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
Yaqin Wang · Journal of Zhejiang University. Science A · 2007
Let K be a closed convex subset of a real reflexive Banach space E, T:K → K be a nonexpansive mapping, and f:K → K be a fixed weakly contractive (may not be contractive) mapping. Then for any t ∈(0, 1), let x t ∈ K be the unique fixed point of the weak contraction x ↦ tf ( x )+(1− t ) Tx . If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E *, then it is shown that { x t } converges to a fixed point of T as t →0. The results presented here improve and generalize the corresponding results in (Xu, 2004).