Solutions rationelles de certaines équations fonctionelles.
Solutions with big graph of iterative functional equations of the second order.
Solutions with big graph of iterative functional equations of the first order
We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,𝜑(x),𝜑(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution 𝜑 has some strange properties: it is dense and connected, has full outer measure and is topologically big.
Solutions with big graph of iterative functional equations of higher orders
Solvability and algorithms for functional equations originating from dynamic programming.
Solvability of the functional equation f = (T-I)h for vector-valued functions
Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and in measure for some f ∈ M(μ;X), then also in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying...
Solving linear functional equations with computer.
Solving some functional and operational equations.
Some aspects of convex functions and their applications.
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 binary representations of real numbers and odd solutions of the functional equation ... .
Some Characterization Theorems for Generalized Measures of Uncertainty and Information.
Some characterizations of q-factorial functions.
Some characterizations of q-factorial functions.
Some complex matrix and determinant functional equations.
Some complex vector systems of partial functional equations
In this paper some types of complex vector systems of partial linear and non-linear functional equations are solved.
Some continuity and approximation properties of a countable iterated function system.
Some discrete Poincaré-type inequalities.
Some Existence Theorems for Functional Equations in Many Variables and the Characterization of Weighted Quasi-Arithmetic Means
Some Existence Theorems for Functional Equations in Many Variables and the Characterization of Weighted Quasi-Arithmetic Means (Short Communication)