Open AccessSome functional equations characterizing polynomials
Author(s) -
Barbara Koclȩga-Kulpa,
Tomasz Szostok,
Szymon Wąsowicz
Publication year - 2009
Publication title -
tatra mountains mathematical publications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.171
H-Index - 12
eISSN - 1338-9750
pISSN - 1210-3195
DOI - 10.2478/v10127-009-0045-2
Subject(s) - mathematics , quadrature (astronomy) , type (biology) , domain (mathematical analysis) , pure mathematics , mathematical analysis , algebra over a field , ecology , biology , electrical engineering , engineering
We present a method of solving functional equations of the typewhere f, F: P → P are unknown functions acting on an integral domain P and parameteresare given. We prove that under some assumptions on the parameters involved, all solutions to such kind of equations are polynomials. We use this method to solve some concrete equations of this type. For example, the equation (1) for f, F: ℝ → ℝ is solved without any regularity assumptions. It is worth noting that (1) stems from a well-known quadrature rule used in numerical analysis.