Continuity properties of sequentially asymptotically center-complete   spaces
  We obtain formulae to calculate the asymptotic center and radius of bounded sequences in ${\cal C}_0(L)$ spaces. We also study the existence of continuous selectors for the asymptotic center map in general Banach spaces. In Hilbert spaces, even a H\"older-type estimation is given. 
C. Angosto, M. C. List\'an-Garc\'ia, F. Rambla-Barreno
math.FA