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9 papers · 2 filters
Some functional equations related to the characterizations of information measures and their stability
Eszter Gselmann, Gyula Maksa
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.
Stability type results concerning the fundamental equation of information of multiplicative type
Eszter Gselmann
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 Hyer…
On the stability of the modified entropy equation
Eszter Gselmann
The aim of this paper is to prove that under some conditions the modified entropy equation is stable on its one-dimensional domain.
Stability of the parametric fundamental equation of information for nonpositive parameters
Eszter Gselmann, Gyula Maksa
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…
On the modified entropy equation
Eszter Gselmann
The object of this paper is to solve the so--called modified entropy equation \[ f<x, y, z>=f<x, y+z, \mathbf{0}>+ μ<y+z>f<\mathbf{0}, \frac{y}{y+z}, \frac{z}{y+z}>, \] on the posi…
Entropy functions and functional equations
Eszter Gselmann
The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we prese…