5 papers · 1 filter
Perturbations of Cauchy differences
Eszter Gselmann, Tomasz MaÅolepszy, Janusz Matkowski
This paper investigates functional equations arising from perturbations of Cauchy differences. We study equations of the form \[ f(x+y)-f(x)-f(y)=B(x,y) \quad \text{or} \quad f(xy)…
Second-order derivations of function spaces -- a characterization of second-order differential operators
WÅodzimierz Fechner, Eszter Gselmann
Let be a nonempty and open set, then for all we have \begin{multline*} \diff{2}{x}(f\cdot g\cdot h) -f\diff{2}{x}(g\cdot h)-…
A direct and algebraic characterization of higher-order differential operators
WÅodzimierz Fechner, Eszter Gselmann
This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extensio…
On Iverson's law of similarity
Eszter Gselmann, Christopher W. Doble, Yung-Fong Hsu
Iverson (2006) proposed the law of similarity \[ ξ_{s}(λx)= γ(λ, s)ξ_{η(λ, s)}(x) \] for the sensitivity functions . Compared to the former models, the ge…
Characterizations of second-order differential operators
WÅodzimierz Fechner, Eszter Gselmann, Aleksandra ÅwiÄ tczak
{Let be positive integers with , and be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ Î(f\cdot g…