Generalization of certain well-known inequalities for rational functions
Abstract
Let
be a class of all polynomials of degree at most m and let
where
and
denote the class of rational functions. It is proved that if the rational function
having all its zeros in
, then for
.
The main purpose of this paper is to improve the above inequality for rational functions
having all its zeros in
with
-fold zeros at the origin and some other related inequalities. The obtained results sharpen some well-known estimates for the derivative and polar derivative of polynomials.








The main purpose of this paper is to improve the above inequality for rational functions



DOI Code:
10.1285/i15900932v40n1p1
Keywords:
Rational functions; Polynomials; Polar derivative; Inequalities; Poles; Restricted Zeros
Full Text: PDF