Dependence properties of solutions on the retardation and initial values in the theory of difference-differential equations

as the retardation h tends to zero, and stated that the same method they used can be applied to demonstrate the corresponding result for more general differentialdifference equations. The author [6] has discussed the same problems as above for general equations (0.1), in which f(ty x, y) is a continuous function denned in a bounded and closed domain and satisfies Lipschitz condition, and he obtained some results as direct consequences of the dependence properties of solutions on the retardation h, as well as the behavior of solutions as h tends to zero. The purpose of this paper is to discuss the problems of dependence properties of solutions of (0.1) on retarded arguments and initial values for the case where t varies in the infinite interval.