David Bellamy has shown
that there exist tree-like continua which do not have the fixed point property. We
give sufficient conditions for a tree-like continuum to have the fixed point property. In
order to establish this result, we define u-mappings on trees and show that each
u-mapping is universal. Our results generalize similar theorems of C. A. Eberhart and
J. B. Fugate in [3].