Comparison inequalities between rational functions with prescribed poles

Abstract

Various versions of Bernstein and Turan-type inequalities are a classical topic in analysis. Over a period, these inequalities have been generalized for different classes of functions. Here, we establish some new comparison inequalities for rational functions in the complex plane that are inspired by some classical inequalities of Bernstein and Turan type. The obtained results produce extensions of many inequalities for polynomials as special cases.