Stability for impulsive delay differential equations

In this paper, the stability for the scalar impulsive delay differential equation y ′ ( t ) + a ( t ) y ( t ) + F ( t , y ( · ) ) = 0 , t ⩾ 0 , t ≠ τ k , y ( τ k + ) - y ( τ k ) = I k ( y ( τ k ) ) , k = 1 , 2 , … , lim k → ∞ τ k = ∞ , 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.