Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping Jφ for some gauge φ. Let Ti:K→K be a family of multivalued nonexpansive mappings with F:=∩i=0∞F(Ti)≠Ø which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. It is our purpose in this paper to prove the convergence of two viscosity approximation schemes to a common fixed point x̄=Qf(x̄) of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, x̄ is the unique solution in F to a certain variational inequality. © 2011 Elsevier Ltd.
Zuo, Z. (2011). Viscosity approximation scheme for a family multivalued mapping. Mathematical and Computer Modelling, 54(9–10), 2423–2427. https://doi.org/10.1016/j.mcm.2011.05.052