Copyright © 2010 A. Kaewkhao and K. Sokhuma. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We introduce a class of nonlinear continuous mappings defined on a bounded closed
convex subset of a Banach space . We characterize the Banach spaces in which every
asymptotic center of each bounded sequence in any weakly compact convex subset is
compact as those spaces having the weak fixed point property for this type of mappings.