Ulam's-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi-Banach Spaces

In this paper, Ulam's-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman-Gronwall-Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of alpha-Holder's condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi-Banach spaces which is best suited for obtaining results under the assumptions of alpha-Holder's condition.