  We study the parameters range for the fixed point of a class of complex
dynamics with the rational fractional function as
$R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c$, where $n=1,2,3,4$ is specified, $a$ and $c$
are two complex parameters. The relationship between two parameters, $a$ and
$c$, is obtained at the fixed point. Moreover the explicit expression of the
parameter $a$ and $c$ in terms of $\lambda$ is derived, where $\lambda$ is the
derivative function at fixed point. The parameter regimes for the stability of
the fixed point are presented numerically for some typical different cases.
