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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## On a functional equation with derivative and symmetrization

### Tom 89 / 2006

Annales Polonici Mathematici 89 (2006), 13-24 MSC: Primary 39B05; Secondary 60G35, 92D10, 47D03. DOI: 10.4064/ap89-1-2

#### Streszczenie

We study existence, uniqueness and form of solutions to the equation $\alpha g - \beta g' + \gamma g_{\rm e} = f$ where $\alpha, \beta, \gamma$ and $f$ are given, and $g_{\rm e}$ stands for the even part of a searched-for differentiable function $g$. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.

#### Autorzy

Katowice branch
Bankowa 14
40-007 Katowice, Poland
and
Department of Mathematics
Faculty of Electrical Engineering
and Computer Science
Lublin University of Technology
20-618 Lublin, Poland
e-mail
• Ma/lgorzata Kubali/nskaDepartment of Computer Sciences
Faculty of Management
and Fundamentals of Technology
Lublin University of Technology