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Iterative approximation of fixed points of nonexpansive mappings with starshaped domain. (English) Zbl 0717.47022
The author studies the iterative process for approximation of a fixed point of a nonexpansive mappings with starshaped domain. His main result reads as follows:
Let E be a reflexive Banach space, which possesses a weakly sequentially continuous duality mapping and A be a closed, bounded subset of E, which is starshaped with respect to zero. Then for each nonexpansive self- mapping T of A the iteration process \(z_{n+1}=\lambda_{n+1}T(z_ n)\) converges to some fixed point of T, if \((\lambda_ n)\) satisfies certain conditions.
Reviewer: B.G.Pachpatte

47H10 Fixed-point theorems
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