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.
Reviewer: L.Górniewicz (Toruń)
MSC:
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
reflexive Banach space; uniformly Gâteaux differentiable norm; nonexpansive mapping; fixed points; strong convergence theoremsReferences:
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