Inequalities for Modulus of Rational Functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 231-236.

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Inequalities for modulus of rational functions with prescribed poles lying in the exterior of the unit disk were obtained in this research. The case when the rational function has no zeros in the unit disk has also been considered.
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S. I. Kalmykov. Inequalities for Modulus of Rational Functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 231-236. http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a8/

[1] N. C. Ankeny, T. J. Rivlin, “On a theorem of S. Bernstein”, Pacific J. Math., 5:suppl. 2 (1955), 849–852 | DOI | MR | Zbl

[2] A. A. Gonchar, “Otsenki rosta ratsionalnykh funktsii i nekotorye ikh prilozheniya”, Matem. sb., 72(114):3 (1967), 489–503 | MR | Zbl

[3] N. K. Govil, R. N. Mohapatra, “Inequalities for Maximum Modulus of Ratioanl Functions with Prescribed Poles”, Approximation Theory: In Memory of A. K. Varma, Marcel Dekker, Inc., New York, 1998, 255–263 | MR | Zbl

[4] M. A. Qazi, “On the maximum modulus of polynomials”, Proc. Amer. Math. Soc., 115:2 (1992), 337–349 | DOI | MR | Zbl

[5] W. M. Shah, A. Liman, “Integral estimates for the family of B-operators”, Operators and matrices, 5:1 (2011), 79–87 | DOI | MR | Zbl

[6] Q. I. Rahman, G. Schmeisser, Analytic theory of polynomials, Oxford University Press, Oxford, 2002 | MR | Zbl

[7] V. N. Dubinin, “O primenenii lemmy Shvartsa k neravenstvam dlya tselykh funktsii s ogranicheniyami na nuli”, Zap. nauchn. sem. POMI, 337 (2006), 101–112 | MR | Zbl

[8] A. A. Gonchar, “O zadachakh E. I. Zolotareva, svyazannykh s ratsionalnymi funktsiyami”, Matem. sb., 78(120):4 (1969), 640–654 | Zbl

[9] S. I. Kalmykov, “Ob otsenke modulya ratsionalnoi funktsii”, Zap. nauchn. sem. POMI, 371 (2009), 109–116 | MR

[10] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M, 1966 | MR

[11] N. K. Govil, Q. I. Rahman, G. Schmeisser, “On the derivative of a polynomial”, Illinois Journal of Mathematics, 23 (1979), 319–329 | MR | Zbl