arXiv subjects

Karol Baron

Publications and source records attributed to Karol Baron.

2 recordsLinked to original sources

arXiv2021

From invariance under binomial thinning to unification of the Cauchy and the Gołąb-Schinzel-type equations

We point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Gołab-Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.

math.CA↗

arXiv2016

Lipschitzian solutions to inhomogeneous linear iterative equations

We study the problems of the existence, uniqueness and continuous dependence of Lipschitzian solutions $φ$ of equations of the form $$ φ(x)=\int_Ωg(ω)φ\big(f(x,ω)\big)μ(dω)+F(x), $$ where $μ$ is a measure on a $σ$-algebra of subsets of a set $Ω$.

math.CA↗