On solutions of functional equations with linear translations
Abstract
In this paper we study the polynomial functional equations of the form $a f(a_1 x +a_0) +b f(b_1 x +b_0)=g(x)$,where g(x) is a polynomial of the degree $n \geq 0$. Theorem \ref{T2.3} affirms that the given equation has a unique polynomial solution provided if $a a_1^i + b b_1^i \not= 0$ for each integer $i \geq 0$. Other non-polynomial solution depends on solutions of the homogeneous equation $a f(a_1 x +a_0) +b f(b_1 x +b_0) = 0$.
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PDFDOI: https://doi.org/10.52846/ami.v45i2.1128