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INEQUALITIES FOR A POLYNOMIAL WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK

  • Received : 2022.01.11
  • Accepted : 2022.04.25
  • Published : 2022.06.30

Abstract

In this paper we prove some results by using a simple but elegant techniques to improve and strengthen some generalizations and refinements of two widely known polynomial inequalities and thereby deduce some useful corollaries.

Keywords

Acknowledgement

This work was supported by DST-INSPIRE.

References

  1. Abdul Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal. Appl., 142 (1989), 1-10. https://doi.org/10.1016/0022-247x(89)90157-1
  2. S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad. Sci. Paris., 190 (1930), 338-340.
  3. C. Frappier, Q. I. Rahman and St. Rusheweyh, New Inequalities for polynomials, Trans. Amer. Math. Soc., 288 (1985), 69-99. https://doi.org/10.2307/2000427
  4. V. N. Dubinin, Applications of the Schwarz Lemma to inequalities for entire functions with constraints on zeros, J. Math. Sci.,(N.Y) 143 (3) (2007), 3069-3076. https://doi.org/10.1007/s10958-007-0192-4
  5. V. N. Dubinin, Distortion theorems for polynomials on the circle, Sbornik: Mathematics, 191 (12) (2000), 1797-1807. https://doi.org/10.1070/SM2000v191n12ABEH000528
  6. P. D. Lax, Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc., 50 (1944), 509-513. https://doi.org/10.1090/S0002-9904-1944-08177-9
  7. M. A. Malik, On the derivative of Polynomial, J. London Math. Soc., 1 (1969), 57-60. https://doi.org/10.1112/jlms/s2-1.1.57
  8. P. Turan, Uber die Ableitung von Polynomen, Compositio Math., 7 (1939), 89-95.
  9. S. L. Wali and W. M. Shah, Some applications of Dubinin's lemma to rational functions with prescribed poles, J. Math. Anal. Appl., 450 (2017), 769-779. https://doi.org/10.1016/j.jmaa.2017.01.069