Viscosity Approximation Methods for Mean Non-Expansive Mappings in Banach Spaces
Yishuai Yang, Yunan Cui · 2014
Abstract. Let C be a nonempty closed convex subset of a real reflexive Banach space X that has weakly continuous duality mapping J. Let T: C → C be a Mean non-expansive mapping with F (T) = ∅. For any t ∈ (0, 1), there exists a sequence {xt} ∈ C satisfying xt = tf(xt)+(1−t)Txt, where f: C → C is a contraction mapping. Then it is proved that {xt} ∈ C converges strongly to a fixed point of T which is also a solution of certain variational inequality.