Strong convergence of approximants to fixed points of nonexpansive nonself-mappings in Banach spaces. (English) Zbl 0947.47049

Let \(E\) be a reflexive Banach space with uniformly Gâteaux differentiable norm, \(C\) a closed convex subset of \(E\) and \(T: C\to C\) be a nonexpansive mapping (or \(T: C\to E\)). In both cases the existence of fixed points is expressed in terms of strong convergence theorems.


47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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