One functional equation with displacement in the space of continuous functions

In the space of continuous functions defined on a simple continuous contour, we examine the functional equationa(t)(t)+b(t)(t)]=g(t) A criterion for Eq. (1) being Noetherian is established under the condition that there exist a finite number of fixed points on the first multiplicity in the homeomorphism (t) of the contour onto itself.Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 303–311, August, 1977.In conclusion, the author thanks G. S. Litvinchuk for guidance on the work.