On an estimate of the decay rate for applications of Razumikhin-type theorems

A decay estimate is established for solutions of a class of Razumikhin-type functional differential equations (FDEs). The FDEs investigated here are general enough to satisfy the requirement of applications of Razumikhin-type theorems. With the help of an application of our result, it is illustrated that the method presented in this paper is adaptable to quantitative stability analysis of the retarded functional differential equations encountered in engineering.