The fixed point property in direct sums and modulus R(a,X)

Authors

  • A. WiÅ›nicki Institute of Mathematics Maria Curie-SkÅ‚odowska University

Keywords:

fixed point theory, nonexpansive mappings

Abstract

We show that the direct sum (X1⊕...⊕Xr)ψ with a strictly monotone norm has the weak fixed point property for nonexpansive mappings whenever M(Xi)>1 for each i=1,...,r. In particular, (X1⊕...⊕Xr)ψ enjoys the fixed point property if Banach spaces Xi are uniformly nonsquare. This combined with the earlier results gives a definitive answer for r=2: a direct sum X1⊕ψX2 of uniformly nonsquare spaces with any monotone norm has the fixed point property. Our results are extended for asymptotically nonexpansive mappings in the intermediate sense. 10.1017/S0004972713000440

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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