Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme

We deal with approximation of solutions delay differential equations (DDEs) via the classical Euler algorithm. investigate pointwise error scheme under nonstandard assumptions imposed on right-hand side function f. Namely, we assume that f is globally at most linear growth, satisfies one-side Lipschitz condition but it only locally Hölder continuous. provide a detailed analysis algorithm such regularity conditions. Moreover, report results numerical experiments.