Bounds on Derivatives in Compositions of Two Rational Functions with Prescribed Poles

TL;DR

This paper derives inequalities for rational functions composed of polynomials and rational functions with specified poles, extending existing bounds and providing new insights into their behavior.

Contribution

It introduces new bounds on derivatives of composed rational functions with prescribed poles, refining previous inequalities in the field.

Findings

Derived new inequalities for derivatives of rational functions with prescribed poles.

Extended existing bounds to a broader class of composed rational functions.

Provided sharper estimates improving upon prior results.

Abstract

This paper explores a class of rational functions r(s(z)) with degree mn, where s(z) is a polynomial of degree m. Inequalities are derived for rational functions with specified poles, extending and refining previous results in the eld.