On the weak-approximate fixed point property
Abstract
Let X be a Banach space and C a bounded, closed, convex subset of X. C is said to have the weak-approximate fixed point property if for any norm-continuous mapping f : C → C, there exists a sequence {xn} in C such that (xn - f (xn))n converges to 0 weakly. It is known that every infinite-dimensional Banach space with the Schur property does not have the weak-approximate fixed point property. In this article, we show that every Asplund space has the weak-approximate fixed point property. Applications to the asymptotic fixed point theory are given. © 2009 Elsevier Inc. All rights reserved.
Publication Title
Journal of Mathematical Analysis and Applications
Recommended Citation
Barroso, C., & Lin, P. (2010). On the weak-approximate fixed point property. Journal of Mathematical Analysis and Applications, 365 (1), 171-175. https://doi.org/10.1016/j.jmaa.2009.10.007
