Geodesic
On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Andrzej Wiśnicki1
1 Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland
Studia Mathematica, Tome 207 (2011) no. 1, pp. 75-84 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $X\oplus Y$ with a strictly monotone norm has the weak fixed point property. The result is new even if $Y$ is finite-dimensional.
DOI : 10.4064/sm207-1-5
Keywords: banach space has weak fixed point property nonexpansive mappings has generalized gossez lami dozo property uniformly convex every direction direct sum oplus strictly monotone norm has weak fixed point property result even finite dimensional

Andrzej Wiśnicki 1

1 Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland 
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Andrzej Wiśnicki. On the fixed points of nonexpansive mappings
 in direct sums of Banach spaces. Studia Mathematica, Tome 207 (2011) no. 1, pp. 75-84. doi: 10.4064/sm207-1-5

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