Fixed points and stability in linear neutral differential equations with variable delays

In this paper we consider the asymptotic stability of a generalized linear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton (2003) 3], Zhang (2005) 14], Raffoul (2004) 13], and Jin and Luo (2008) 12]. Two examples are also given to illustrate our results.