Hyers-Ulam Stability of the Delay Equation y'(t)=y(t-)

and Applied Analysis 3 we describe a behavior of solutions of the following problem the delay differential inequality with an initial condition ε1 ≤ y′ t − λy t − τ ≤ ε2, t ≥ 0, 1.5 ξ1 t ≤ y t − y 0 ≤ ξ2 t , −τ ≤ t ≤ 0, 1.6 and compare them with solutions of the delay equation 1.4 that are constant on the interval −τ, 0 and therefore have quite simple forms . Functions satisfying those two inequalities may be considered to be approximate solutions of 1.4 . 2. An Auxiliary Theorem Let us recall a description of a class of solutions of 1.4 . Remark 2.1. It is known that if λ/ 0 and τ > 0 are real constants, then the general solution y : −τ,∞ → R of the delay differential equation 1.4 , which is constant on the interval −τ, 0 , is given by