On the functional-differential equation of advanced type f (x) = af (λx), λ>1, with f (0) = 0

Solutions to the equation f (x) = af (λx), x ∈ R, f (0) = 0, are constructed for constants λ > 1 and a = 0. The solutions are infinitely differentiable and have some symmetry. By our method, numerical computations can be made effectively. © 2006 Elsevier Inc. All rights reserved