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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 4, 1991, pp. 417–431
DOI: 10.4171/ZAA/464

Published online: 1991-12-31

A Fixed Point Theorem for Non-Expansive Mappings on Star-Shaped Domains

Jürgen Schu

It is shown that some modification of the fixed point theorem of Browder, Gohde and Kirk remains valid on star-shaped domains as well. Additionally, we will give an iteration scheme for the approximation of some fixed point of the mapping under consideration. Finally, in connection with the result above, two characterizations of inner product spaces will be obtained.

Keywords: fixed points, tear-shaped sets, nonexpansive and pseudocontractive mappings, characterisations of inner product spaces

Schu Jürgen: A Fixed Point Theorem for Non-Expansive Mappings on Star-Shaped Domains. Z. Anal. Anwend. 10 (1991), 417-431. doi: 10.4171/ZAA/464