Open AccessEstimates for the maximal modulus of rational functions with prescribed poles
Author(s) -
Gradimir V. Milovanović,
Abdullah Mir,
Abrar Ahmad
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105511m
Subject(s) - mathematics , lemma (botany) , rational function , mathematical proof , modulus , pure mathematics , function (biology) , mathematical analysis , geometry , poaceae , evolutionary biology , ecology , biology
In this paper, we obtain certain sharp estimates for the maximal modulus of a rational function with prescribed poles. The proofs of the obtained results are based on the new version of the Schwarz lemma for regular functions which was suggested by Osserman. The obtained results produce several inequalities for polynomials as well.