Solving some functional and operational equations.
Some aspects of the local theory of generalized Dhombres functional equations in the complex domain
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...
Some continuity and approximation properties of a countable iterated function system.
Some functional inequalities and their Baire category properties.
Some functional inequalities and their Baire category properties. (Summary).
Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number
We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]).
Stability of Jungck-type iterative procedures.
Stability of normal regions for linear homogenous functional equations.
Strictly decreasing solutions of a class of iterative equations on the unit circle.
Subgroups of the group Zn and a generalization of the Golab-Schinzel functional equation.
Substitution systems associated with the dynamical system (𝒜, Tf)*
We consider the dynamical system (𝒜, Tf), where 𝒜 is a class of differential real functions defined on some interval and Tf : 𝒜 → 𝒜 is an operator Tfφ := fοφ, where f is a differentiable m-modal map. If we consider functions in 𝒜 whose critical values are periodic points for f then, we show how to define and characterize a substitution system associated with (𝒜, Tf). For these substitution systems, we compute the growth rate of the...
Sur la caractérisation de la fonction f(x) = x par des équations fonctionnelles, II. (Short Communication).
Sur les équations fonctionelles aux itérées.
Sur les équations fonctionelles aux q-différences.
Sur les équations fonctionnelles qui caractérisent les opérations associatives et les opérations distributives
Sur un problème au sujet des homomorphismes.
Sur une classe des groupes continus à un paramètre formés des fonctions réelles d'une variable
Sur une forme de familles de fonctions commutatives
The solutions of the series-like iterative equation with variable coefficients.
The continuous solutions of a generalized Dhombres functional equation
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under and which contains in its interior no fixed point except for . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for any solution...