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Nonexpansive mappings in metric and Banach spaces

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Abstract

The fundamental fixed point theorem for nonexpansive mappings is reformulated in the setting of a metric space possessing a convexity structure, and various constructive and nonconstructive proofs are compared. A new proof of the Browder-Göhde demiclosedness principle for mappings of the formI–T, T nonexpansive, is given, and a related result of R. E. Bruck in discussed.

Sunto

Si riformula, nel contesto di uno spazio metrico che possiede una struttura di convessità, il teorema fondamentale di punto fisso per applicazioni non espansive e si confrontano fra loro varie dimostrazioni, di tipo costruttivo e non costruttivo, di questo teorema. Viene inoltre data una nuova dimostrazione del principio di demichiusura di Browder-Göhde per applicazioni della formaI–T (T non espansiva) e viene discusso un risultato di R. E. Bruck ad esso correlato.

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Authors and Affiliations

  1. dell’Università dell’Iowa, USA

    W. A. Kirk

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  1. W. A. Kirk
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(Conferenza tenuta il 25 maggio 1981)

Partially supported by National Science Foundation Grant MCS 80-01604.

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Kirk, W.A. Nonexpansive mappings in metric and Banach spaces. Seminario Mat. e. Fis. di Milano 51, 133–144 (1981). https://doi.org/10.1007/BF02924816

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