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Abstract

In this paper we prove someL P inequalities for polynomials, wherep is any positive number. They are related to earlier inequalities due to A Zygmund, N G De Bruijn, V V Arestov, etc. A generalization of a polynomial inequality concerning self-inversive polynomials, is also obtained.

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References

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

    MathSciNet  Google Scholar 

  2. Arestov V V, On integral inequalities for trigonometric polynomials and their derivatives,Izv. Akad. Nauk SSR Sen Mat. 45 (1981) 3–22 [in Russian]; English translation:Math. USSR Izv. 18 (1982) 1–17

    MathSciNet  Google Scholar 

  3. Arestov V V, Integral inequalities for algebraic polynomials with a restriction on zeros,Anal. Math. 17(1991) 11–20

    Article  MATH  MathSciNet  Google Scholar 

  4. Aziz A, A new proof and a generalization of a theorem of De Bruijn,Proc. Am. Math. Soc. 106 (2) (1989) 345–350

    Article  MATH  MathSciNet  Google Scholar 

  5. Aziz A and Rather N A,L p inequalities for polynomials,Glas. Mat. 32 (52) (1997) 39–43

    MATH  MathSciNet  Google Scholar 

  6. Boas Jr. R P and Rahman Q I,LP inequalities for polynomials and entire functions,Arch. Rational Mech. Anal. 11 (1962) 34–39

    Article  MATH  MathSciNet  Google Scholar 

  7. De Bruijn N G, Inequalities concerning polynomials in the complex domain,Ned. Akad. Wetensch, Proc. 50 (1947) 1265–1272Indag. Math. 9 (1947) 591–598.

    MATH  Google Scholar 

  8. Dewan K K and Govil N K, An inequality for self-inversive polynomials,J. Math. Anal. Appl. 95 (1983) 490

    Article  MathSciNet  MATH  Google Scholar 

  9. Hardy G H, The mean value of the modulus of an analytic function,Proc. Lond. Math. Soc. 14 (1915) 269–277

    Google Scholar 

  10. Lax P D, Proof of a conjuncture of P Erdös on the derivative of a polynomial,Bull. Am. Math. Soc. 50 (1944) 509–513

    Article  MATH  MathSciNet  Google Scholar 

  11. Milovanovic G V, Mitrinovic D S and Rassias Th M,Topics in Polynomials: Extremal Properties, Inequalities, Zeros. World Scientific Publishing Co. Singapore (1994)

    Google Scholar 

  12. Polya G and Szegö G,Problems and Theorems in Analysis, Vol. I, Springer-Verlag, New York (1972)

    MATH  Google Scholar 

  13. Rahman Q I and Schmeisser G,Les inégalités de Markoff et de Bernstein, Presses Univ. Montréal, Montréal, Québec (1983)

    MATH  Google Scholar 

  14. Rahman QI and Schmeisser G,L p inequalities for polynomials,J. Approx. Theory 53 (1988) 26–32

    Article  MATH  MathSciNet  Google Scholar 

  15. Riesz M, Formula d’interpolation pour la dérivée d’un polyome trigonométrique,C R Acad. Sci. Paris 158 (1914) 1152–1154

    Google Scholar 

  16. Riesz M, Über einen satz des Herrn Serge Bernstein,Acta Math. 40 (1916) 337–347

    Article  MathSciNet  MATH  Google Scholar 

  17. Schaeffer A C, Inequalities of A Markoff and S Bernstein for polynomials and related functions,Bull. Am. Math. Soc. 47 (1941) 565–579

    MATH  MathSciNet  Google Scholar 

  18. Szegö G, Bemerkungen zu einem Satz von J H Grace Über die wurzeln algebraischer Gleichungen,Math. Z. 13 (1922) 28–55

    Article  MathSciNet  Google Scholar 

  19. Zygmund A, A remark on conjugate series,Proc. London Math. Soc. (2)34 (1932) 392–400

    Article  MATH  MathSciNet  Google Scholar 

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Aziz, A., Rather, N.A. New integral mean estimates for polynomials. Proc. Indian Acad. Sci. (Math. Sci.) 109, 65–74 (1999). https://doi.org/10.1007/BF02837768

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  • DOI: https://doi.org/10.1007/BF02837768

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