Somarakis, ChristoforosBaras, JohnParaskevas, EvripidisWe discuss the dynamics of general linear functional differential equations with solutions that exhibit asymptotic constancy. We apply fixed point theory methods to study the stability of these solutions and we provide sufficient conditions of asymptotic stability with emphasis on the rate of convergence. Several examples are provided to illustrate the claim that the derived results generalize, unify and in some cases improve the existing ones.en-USFixed PointsStabilityRate of ConvergenceDelaysTechnical Report