We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-3-5,
author = {Andrzej Wi\'snicki},
title = {The super fixed point property for asymptotically nonexpansive mappings},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {265-277},
zbl = {1270.47047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-3-5}
}
Andrzej Wiśnicki. The super fixed point property for asymptotically nonexpansive mappings. Fundamenta Mathematicae, Tome 219 (2012) pp. 265-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-3-5/