Geodesic
Some inequalities for maximum modulus of rational functions
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 1, pp. 33-39.

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In this paper, we establish some inequalities for rational functions with prescribed poles and restricted zeros in the sup-norm on the unit circle in the complex plane. Generalizations and refinements of rational function inequalities of Govil, Li, Mohapatra and Rodriguez are obtained.
Keywords: Rational function, polynomial, poles, zeros 
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Mir, Abdullah. Some inequalities for maximum modulus of rational functions. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 73 (2019) no. 1, pp. 33-39. http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a0/

[1] Ankeny, N. C., Rivlin, T. J., On a theorem of S. Bernstein, Pacific J. Math. 5 (1955), 849–852.

[2] Aziz, A., Dawood, Q. M., Inequalities for a polynomial and its derivatives, J. Approx. Theory 54 (1998), 306–313.

[3] Bernstein, S., Sur l’ordre de la meilleure approximation des functions continues par des polynomes de degre donne, Mem. Acad. R. Belg. 4 (1912), 1–103.

[4] Govil, N. K., Mohapatra, R. N., Inequalities for maximum modulus of rational functions with prescribed poles, in: Approximation Theory, Dekker, New York, 1998, 255–263.

[5] Lax, P. D., Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509–513.

[6] Xin Li, A comparison inequality for rational functions, Proc. Amer. Math. Soc. 139 (2011), 1659–1665.

[7] Xin Li, Mohapatra, R. N., Rodriguez, R. S., Bernstein-type inequalities for rational functions with prescribed poles, J. London Math. Soc. 51 (1995), 523–531.