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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 4, 2002, pp. 901–914
DOI: 10.4171/ZAA/1116

Published online: 2002-12-31

On the Minimal Displacement Problem of $\gamma$-Lipschitz Maps and $\gamma$-Lipschitz Retractions onto the Sphere

Martin Väth[1]

(1) Czech Academy of Sciences, Prague, Czech Republic

We give a general construction in arbitrary normed spaces to produce fixed-point free continuous maps with a large minimal displacement, contractions of the sphere, and retractions onto the sphere such that the corresponding maps have small measures of non-compactness.

Keywords: Condensing operator, measure of non-compactness, fixed point, minimal displacement, retraction

Väth Martin: On the Minimal Displacement Problem of $\gamma$-Lipschitz Maps and $\gamma$-Lipschitz Retractions onto the Sphere. Z. Anal. Anwend. 21 (2002), 901-914. doi: 10.4171/ZAA/1116