Hyers–Ulam stability of linear differential equations of first order, II

Let XX be a complex Banach space and let II be an open interval. For given functions g:I→Cg:I→C, h:I→Xh:I→X and φ:I→[0,∞)φ:I→[0,∞), we will solve the differential inequality ‖y′(t)+g(t)y(t)+h(t)‖≤φ(t)‖y′(t)+g(t)y(t)+h(t)‖≤φ(t) for the class of continuously differentiable functions y:I→Xy:I→X under some integrability conditions.