Some applications of transform which map derivatives into generalized differences
We study the generalized Dhombres functional equation f(zf(z)) = ϕ(f(z)) in the complex domain. The function ϕ is given and we are looking for solutions f with f(0) = w0 and w0 is a primitive root of unity of order l ≥ 2. All formal solutions for this case are described in this work, for the situation where ϕ can be transformed into a function which is linearizable and local analytic in a neighbourhood of zero we also show...
We study k th order systems of two rational difference equations . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.
In this paper some types of complex vector systems of partial linear and non-linear functional equations are solved.
In the present paper some complex vector functional equations of higher order without parameters and with complex parameters are solved.