Ulam stability for a delay differential equation (Q1955614)

The paper is concerned with the stability analysis of delay equations of the general form \[ x'(t)=f(t,x(t),x(g(t))),\;g(t) \leq t. \] The work begins with a summary of important definitions, and introduces the stability concepts to be considered. Two main results are provided, the Ulam-Hyers stability of the solution on a compact interval \([a,b]\) and the generalised Ulam-Hyers-Rassias stability on an interval \([a, \infty).\) The paper concludes with some examples and applications of the theory.