Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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BERNSTIEN AND TURÁN TYPE INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL

  • N. Reingachan (Department of Mathematics, National Institute of Technology Manipur) ;
  • Barchand Chanam (Department of Mathematics, National Institute of Technology Manipur)
  • Received : 2022.06.06
  • Accepted : 2022.07.31
  • Published : 2023.03.03
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Abstract

The goal of this paper is to extend some inequalities of Bernstein as well as Turán type to polar derivative of a polynomial.

Keywords

Acknowledgement

We are grateful to the referees for their useful suggestions.

References

  1. A. Aziz, Inequalities for the polar derivative of a polynomial, J. Approx. Theory, 55(2) (1988), 183-193. https://doi.org/10.1016/0021-9045(88)90085-8
  2. A. Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal. Appl., 144(1) (1989), 226-235. https://doi.org/10.1016/0022-247x(89)90370-3
  3. S. Bernstein, Sur la limitation des d'eriv'ees des polynomes, Comptes rendus de l'Acad'emie des Sciences, 190 (1930), 338-340.
  4. V.N. Dubinin, Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros, J. Math. Sci., (New York), 143(3) (2007), 3069-3076. https://doi.org/10.1007/s10958-007-0192-4
  5. C. Frappier, Q.I. Rahman and St. Ruscheweyh, New inequalities for polynomials, Trans. Amer. Math. Soc., 288 (1985), 69-99. https://doi.org/10.1090/S0002-9947-1985-0773048-1
  6. N.K. Govil and Q.I. Rahman, Functions of exponential type not vanishing in a half-plane and related polynomials, Trans. Amer. Math. Soc., 137 (1969), 501-517. https://doi.org/10.2307/1994818
  7. 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
  8. M. Marden, Geometry of Polynomials, Math. Surveys, Vol. 3, Amer. Math. Soc., Providence, 3 1966.
  9. G.V. Milovanovic, D.S. Mitrinovic and T.M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific., Singapore, 1994.
  10. G. Polya and G. Szego, Problems and theorems in analysis, New York: Springer, 1 1972.
  11. W.M. Shah, A generalization of a theorem of Paul Turan, J. Ramunujan Math. Soc., 11(1) (1996), 67-72.
  12. P. Turan, Uber die ableitung von polynomen, Composition Math., 7 (1939), 89-95.
  13. S.L. Wali and W.M. Shah, Bernstein type inequalities for polynomials with restricted zeros, J. Anal., 29 (2021), 1083-1091, https://doi.org/10.1007/s41478-020-00296-0.