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Viscosity approximation methods for nonexpansive multimaps in Banach spaces. (English) Zbl 1216.47105

The paper proves strong convergence results by a viscosity approximation process for a nonexpansive nonself multivalued mapping \(T\) with compact values in uniformly convex Banach spaces. The hypotheses of the results do not contain a condition on the existence of a strict fixed point for \(T\).

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
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References:

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