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.
A. Kaewkhao. K. Sokhuma. "Remarks on Asymptotic Centers and Fixed Points." Abstr. Appl. Anal. 2010 1 - 5, 2010. https://doi.org/10.1155/2010/247402