Geodesic
Bernstein type inequalities for one class of complex rational functions
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 49 (2024), p. 31

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this study, we establish some Bernstein-type norm estimates for a rational function and its derivative on the unit circle. The estimates involve the positioning of all the zeros of the rational function and the poles are assumed to lie outside the unit circle. Our results strengthen some existing bounds and additionally derive a polynomial inequality pertinent to the Saff conjecture. Numerical examples are included.
Classification : 30A10, 30C15, 30D15
Keywords: Bernstein type inequalities, rational function, algebraic polynomial, zeros and poles, finite Blaschke product, polar derivative 
Gradimir V. Milovanović; Abdullah Mir; Idrees Qasim; See Keong Lee. Bernstein type inequalities for one class of complex rational functions. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 49 (2024), p. 31 . http://geodesic.mathdoc.fr/item/BASS_2024_49_a3/
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     title = {Bernstein type inequalities for one class of complex rational functions},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {31 },
     year = {2024},
     volume = {49},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2024_49_a3/}
}
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