Abstract
Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping J φ for some gauge φ . Let T i : K → K be a family of multivalued nonexpansive mappings with F : = ∩ i = 0 ∞ F ( T i ) ≠ 0̸ 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 x ̄ = Q f ( x ̄ ) of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, x ̄ is the unique solution in F to a certain variational inequality.
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