Far Eastern Mathematical Journal

To content of the issue

Inequalities for derivatives of rational functions with critical values on an interval

Dubinin V. N.

2024, issue 2, P. 187-192 DOI: https://doi.org/10.47910/FEMJ202417

Abstract

Multipoint distortion theorems are proved for rational functions with restrictions on their zeros, poles and critical values.

Keywords: polynomials, rational functions, critical values, inequalities for derivatives.

Download the article (PDF-file)

References

[1] Rusak V. N., Rat?sional?nye funkt?sii kak apparat priblizheniia, BGU, Minsk, 1979. [2] Borwein P., Erd`elyi T., “Sharp extensions of Bernstein’s inequality to rational spaces”, Mathematika, 43, (1996), 413–423. [3] Min G., “Inequalities for rational functions with prescribed poles”, Can. J. Math., 50:1, (1998), 152–166. [4] Dubinin V. N., “O primenenii konformnykh otobrazheni? v neravenstvakh dlia rat?sional?nykh funkt?si?”, Izv. RAN. Ser. matem., 66:2, (2002), 67–80. [5] Lukashov A. L., “Neravenstva dlia proizvodnykh rat?sional?nykh funkt?si? na neskol?kikh otrezkakh”, Izv. RAN. Ser. matem., 68:3, (2004), 115–138. [6] Kalmykov S., Nagy B., Totik V., “Bernstein and Markov type inequalities for rational functions”, Acta Math., 219, (2017), 21–63. [7] Wali S. L., Shah W. M., “Some applications of Dubinin’s lemma to rational functions with prescribed poles”, J. Math. Anal. Appl., 450:1, (2017), 769–779. [8] Kalmykov S. I., “O mnogotochechnykh teoremakh iskazheniia dlia rat?sional?nykh funkt?si?”, Sib. matem. zhurn., 61:1, (2020), 107–119. [9] Dubinin V. N., “O polinomakh s kriticheskimi znacheniiami na otrezke” , Matem. zametki, 78:6, (2005), 827–832. [10] Dubinin V. N., Condenser capacities and symmetrization in geometric function theory, Birkhauser/ Springer, Basel, 2014. [11] Goluzin G. M., Geometricheskaia teoriia funkt?si? kompleksnogo peremennogo, Nauka, M., 1966.

To content of the issue