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

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

2011-11-29

arxiv.org/abs/1111.6965v1

Studia Mathematica 207 (2011), 75-84

Mathematics

Functional Analysis

9 pages. To appear, Studia Mathematica

Scientific paper

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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