We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-6, author = {P. N. Dowling and C. J. Lennard and B. Turett}, title = {New fixed point free nonexpansive maps on weakly compact, convex subsets of L$^1$[0,1]}, journal = {Studia Mathematica}, volume = {178}, year = {2007}, pages = {271-284}, zbl = {1125.47040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-6} }
P. N. Dowling; C. J. Lennard; B. Turett. New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]. Studia Mathematica, Tome 178 (2007) pp. 271-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-6/