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

Abstract

We show that the direct sum of Banach spaces $X_1,...,X_r$ with a strictly monotone norm has the weak fixed point property for nonexpansive mappings whenever $M(X_i)>1$ for each $i=1,...,r$. In particular, $(X_1\oplus ...\oplus X_r{)}_{\psi }$ enjoys the fixed point property if Banach spaces $X_i$ are uniformly nonsquare. This combined with the earlier results gives a definitive answer for r=2: the direct sum of uniformly nonsquare spaces $X_1,X_2$ with any monotone norm has FPP. Our results are extended for asymptotically nonexpansive mappings in the intermediate sense.

12 pages

References in corpus (2)

• The super fixed point property for asymptotically nonexpansive mappings
• On the fixed points of nonexpansive mappings in direct sums of Banach spaces

Cited by in corpus (1)

• Hyper-extensions in metric fixed point theory