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arXiv · 1111.6965

On the fixed points of nonexpansive mappings in direct sums of Banach spaces

Andrzej Wiśnicki
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Abstract

We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum of X and Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.

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Andrzej Wiśnicki. 2011-11-29. On the fixed points of nonexpansive mappings in direct sums of Banach spaces. https://doi.org/10.4064/sm207-1-5

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