On a canonical two-dimensional space of continuous functions
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained,...
The paper describes the general form of functional-differential equations of the first order with delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation for is solved on and a method of proof by J. Aczél is applied.
The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form is solved on for ,