Acta Mathematica Vietnamica
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A BOUNDED 2-HYPERCONVEX SPACE FAILING TO HAVE THE FIXED POINT PROPERTY FOR A STRICTLY NON-EXPANSIVE MAP
NGUYEN NHUYpp. 15-26
Abstract
It was shown in [3] that if $\lambda < 2$, then any bounded $\lambda$-hyperconvex space has the fixed point property for non-expansive maps. In this note we construct an example of a bounded 2-hyperconvex space with the fixed point free for any iteration of a strictly non-expansive map.