Stability for impulsive delay differential equations

In this paper, the stability for the scalar impulsive delay differential equationy′(t)+a(t)y(t)+F(t,y(·))=0,t⩾0,t≠τk,y(τk+)-y(τk)=Ik(y(τk)),k=1,2,…,limk→∞τk=∞,where delay arguments may be bounded or unbounded is investigated. Some new stability theorems are established which improve and extend several known results in the literature.