Analytic solutions of an iterative functional equation
Tóm tắt
This paper is concerned with the functional equation
f
(p
(z) +
bf
(z)) =
h
(z) for
f.
By constructing a convergent power
series solution of an auxiliary equation of the form
$$ g\left(\beta ^{2}z\right) -p\left(g(\beta z)\right) =bh\left( g(z)\right), $$
analytic solutions of the form
$$ f(z) = \left\{ g\left( \beta g^{-1}(z)\right) -p(z)\right\} /b $$
for the original equation are obtained.