On solutions of functional equations with polynomial translations

Autor:	Larisa M. Sali, Mitrofan M. Choban
Rok vydání:	2019
Předmět:	Polynomial Applied mathematics Ocean Engineering Mathematics
Zdroj:	Creative Mathematics and Informatics. 28:53-59
ISSN:	1843-441X 1584-286X
DOI:	10.37193/cmi.2019.01.08
Popis:	In this paper, we study polynomial functional equations of the form af(p(x)) + bf(q(x)) = g(x), where p(x), q(x) are given polynomials and g(x) is a given function. Theorems 21 and 22 contain sufficient conditions under which the functional equation has a solution of the special form. In Section 3 we present an algorithm of constructing polynomial solutions of the functional equations. Other non-polynomial solutions depend on solutions of the homogeneous equation af(p(x)) + bf(q(x)) = 0. That case is analyzed in Section 4. Finally, we present a simple method of constructing examples with desirable properties.
Databáze:	OpenAIRE
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