## Strong convergence of viscosity iteration methods for nonexpansive mappings.(English)Zbl 1168.47053

Summary: We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for the viscosity iterative scheme are given and the strong convergence of the viscosity iterative scheme to a solution of a certain variational inequality is established.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47J20 Variational and other types of inequalities involving nonlinear operators (general)
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### References:

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