In this brief, by constructing an augmented Lyapunov-Krasovskii functional in a triple integral form, the stability analysis of delayed neural networks is investigated. In order to exploit more accurate bounds for the derivatives of triple integrals, new double integral inequalities are developed, which include some recently introduced estimation techniques as special cases. The information on the activation function is taken into full consideration. Taking advantages of the proposed inequalities, the stability criteria with less conservatism are derived. The improvement of the obtained approaches is verified by numerical examples.