Rouche's theorem

Rouche's theorem

[′rüsh·əz ‚thir·əm]
(mathematics)
If analytic functions ƒ(z) and g (z) in a simply connected domain satisfy on the boundary | g (z)| <>z)| , then ƒ(z) and ƒ(z) + g (z) have the same number of zeros in the domain.
References in periodicals archive ?
1/2] - 1 for sufficiently large h, hence Rouche's theorem (where we compare [R.
2](t) has the unique zero t = 1/2 in the disk [absolute value of t] < r, it follows from Rouche's theorem that h(t) also has the unique zero in the disk [absolute value of t] < r.
By Rouche's Theorem, the transcendental equation (i) has roots with positive real parts if and only if it has purely imaginary roots.
By Rouche's Theorem, the real parts of all the eigenvalues of the characteristic equation corresponding to equilibrium point B are negative for all delay [tau] > 0.
Using general form of Rouche's Theorem we conclude that r(z) - r([beta]) has only a simple zero at [beta].
An application of the principle of the argument or Rouche's Theorem shows such a root to exist with all other roots of modulus greater than 3/4.