Stability in neutral nonlinear dynamic equations on a time scale with functional delay

Let T be a time scale that is unbounded above and below and such that 0 is an element of T. Let tau : T -> T be such that tau(T) is a time scale. We use fixed point theorems to obtain stability results about the zero solution of the nonlinear neutral dynamic equation with functional delay x(Delta)(t) = -a(t)x(sigma)(t) + c(t)x((Delta) over bar)(tau(t)) + q(x(t), x(tau(t))), t is an element of T, where f(Delta) is the Delta-derivative on T and f((Delta) over bar) is the A-derivative on tau(T).