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math.CA2026
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)…
math.CA2026
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)-…