Some inequalities for maximum modulus of rational functions

Abdullah Mir

Abstract


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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References


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

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

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.

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.

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

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

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.




DOI: http://dx.doi.org/10.17951/a.2019.73.1.33-39
Date of publication: 2019-12-19 10:33:46
Date of submission: 2019-12-17 09:57:34


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