Viscosity approximation scheme for a family multivalued mapping

نویسنده

  • Zhanfei Zuo
چکیده

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) ≠ ∅ 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. All rights reserved.

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عنوان ژورنال:
  • Mathematical and Computer Modelling

دوره 54  شماره 

صفحات  -

تاریخ انتشار 2011