Eszter Gselmann

Hyperstability of a functional equation

The aim of this paper is to prove that the parametric fundamental equation of information is hyperstable on its open as well as on its closed domain, assuming that the parameter is negative. As a corollary of the main result, it is also proved that the system of equations that defines the alpha-recursive information measures is stable.

Hyers–Ulam stability of derivations and linear functions

In this paper the following implication is verified for certain basic algebraic curves: if the additive real function f approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in consideration, then f can be represented as the sum of a derivation and a linear function. When, instead of the additivity of f, it is assumed that, in addition, the Cauchy difference of f is bounded, a stability theorem is obtained for such characterizations of derivations.

Derivations and linear functions along rational functions

The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let

Stability type results concerning the fundamental equation of information of multiplicative type

{n \in \mathbb{Z}, f, g\colon\mathbb{R} \to\mathbb{R}}

Approximate Derivations of Order n

be additive functions,

Some Functional Equations Related to the Characterizations of Information Measures and Their Stability

{\left(\begin{array}{cc} a&b\\ c&d \end{array} \right) \in \mathbf{GL}_{2}(\mathbb{Q})}