... fixed point of P. After showing thecompactness of the Poincar´e operator P and obtaining the boundedness of the fixed point set{x λPx, λ ∈ 0, 1} by virtue of the generalized Gronwall inequality, ... 3.12Similar to the proof in i, one can obtainxt≤xtB≤ aebdt. 3.13Combining i and ii, one can complete the proof.Using Gronwall’s inequality with impulse and B-norm, ... 4.1722 Journal of Inequalities and Applications19 Y. Peng, X. Xiang, and W. Wei, “Nonlinear impulsive integro-differential equations of mixed typewith time-varying generating operators and optimal...