Inequalities for complex rational functions. (English) Zbl 1435.30021

Summary: In this paper, we consider a class of rational functions \(r(s(z))\) of degree at most \(mn\), where \(s(z)\) is a polynomial of degree \(m\) and obtain a certain sharp compact generalization of well-known inequalities for rational functions.


30C10 Polynomials and rational functions of one complex variable
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
30A10 Inequalities in the complex plane
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