73 citations · 119 across the 38 of their papers we have counts for
44 papers
Perturbations of Cauchy differences
Eszter Gselmann, Tomasz Małolepszy, 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)…
A direct and algebraic characterization of higher-order differential operators
Włodzimierz 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…
Second-order derivations of function spaces -- a characterization of second-order differential operators
Włodzimierz 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)-g\…
A functional equation for monomial functions
Eszter Gselmann, Mehak Iqbal
Let be fields with characteristic zero, be a positive integer and . In this paper, we determine those monomials $f\colon \mathbb…
Quadratic functions as solutions of polynomial equations
Eszter Gselmann, Mehak Iqbal
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relative…
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 generality…