arXiv subjects
Publications and source records attributed to Eszter Gselmann.
In this note we give a characterization of a family of relative entropies on open domain depending on a real parameter $α$ based on recursivity and symmetry. In the cases $α=1$ and $α=0$ we use additionally a weak regularity assumption while in the other cases no regularity assumptions are made at all.
In one of his work, appeared in 1969, John A. Baker initiated the systematic investigation of some partial difference equations. The main purpose of this paper is to continue and to extend these investigations. Firstly, we present how such type of equations can be classified into elliptic, parabolic and hyperbolic subclasses, respectively. After that, we show solution methods in the elliptic class. Here we will deal in details with the discrete version of the following partial differential equations: Laplace's equation, Poisson equation and the (in)homogeneous biharmonic equation.
The main purpose of this paper is to investigate the stability problem of some functional equations that appear in the characterization problem of information measures.
In this note we prove that the parametric fundamental equation of information is stable in the sense of Hyers and Ulam provided that the parameter is nonpositive. We also prove, as a corollary, that the system of equations that defines the recursive and semi-symmetric information measures depending on a nonpositive parameter is stable in a certain sense.
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.
The aim of this paper is to prove that under some conditions the modified entropy equation is stable on its one-dimensional domain.
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 $n\in\mathbb{Z}$, $f, g\colon\mathbb{R}\to\mathbb{R}$ be additive functions, $<{array}{cc} a&b c&d {array}>\in\mathbf{GL}_{2}(\mathbb{Q})$ be arbitrarily fixed, and let us assume that the mapping \[ ϕ(x)=g<\frac{ax^{n}+b}{cx^{n}+d}>-\frac{x^{n-1}f(x)}{(cx^{n}+d)^{2}} \quad \] satisfies some regularity on its domain (e.g. (locally) boundedness, continuity, measurability). Is it true that in this case the above functions can be represented as a sum of a derivation and a linear function? Analogous statements ensuring linearity will also be presented.
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 equation that defines the alpha-recursive information measures is stable.
The paper deals with the stability of the fundamental equation of information of multiplicative type. It will be proved that the equation in question is stable in the sense of Hyers and Ulam under some assumptions. This result will be applied to prove the stability of a system of functional equations that characterizes the recursive measures of information of multiplicative type.