Research ArticleOpen AccessGoogle Scholar indexed
<i>L<sup>p</sup></i> Inequalities for Polynomials
- 1
- 2
Copy link · social · email
Abstract
In this paper we consider a problem of investigating the dependence of on for every real or complex number with , , and present certain compact generali- zations which, besides yielding some interesting results as corollaries, include some well-known results, in particular, those of Zygmund, Bernstein, De-Bruijn, Erdös-Lax and Boas and Rahman as special cases.
Keywords<i>L<sup>p</sup></i>-InequalitiesPolynomialsComplex Domain
- G. V. Milovanovic, D. S. Mitrinovic and T. M. Rassias, “Topics in Polynomials: Extremal Properties, Inequalities, Zeros,” World Scientific Publishing Company, Singapore, 1994.
- A. C. Schaffer, “Inequalities of A. Markoff and S. Bernstein for Polynomials and Related Functions,” Bulletin American Mathematical Society, Vol. 47, No. 2, 1941, pp. 565-579. doi:10.1090/S0002-9904-1941-07510-5
- G. Pólya and G. Szeg?, “Aufgaben und Lehrs?tze aus der Analysis,” Springer-Verlag, Berlin, 1925.
- A. Zygmund, “A Remark on Conjugate Series,” Proceedings of London Mathematical Society, Vol. 34, 1932, pp. 292-400. doi:10.1112/plms/s2-34.1.392
- G. H. Hardy, “The Mean Value of the Modulus of an Analytic Function,” Proceedings of London Mathematical Society, Vol. 14, 1915, pp. 269-277.
- Q. I. Rahman and G. Schmeisser, “Les in Ualitués de Markoff et de Bernstein,” Presses University Montréal, Montréal, 1983.
- M. Riesz, “Formula d’interpolation Pour la Dérivée d’un Polynome Trigonométrique,” Comptes Rendus de l' Academie des Sciences, Vol. 158, 1914, pp. 1152-1254.
- V. V. Arestov, “On Integral Inequalities for Trigonometric Polynimials and Their Derivatives,” Mathematics of the USSR-Izvestiya, Vol. 18, 1982, pp. 1-17. doi:10.1070/IM1982v018n01ABEH001375
- N. G. Bruijn, “Inequalities Concerning Polynomials in the Complex Domain,” Nederal. Akad. Wetensch. Proceeding, Vol. 50, 1947, pp. 1265-1272.
- Q. I. Rahman and G. Schmessier, “ Inequalities for Polynomials,” The Journal of Approximation Theory, Vol. 53, 1988, pp. 26-32. doi:10.1016/0021-9045(88)90073-1
- R. P. Boas, Jr., and Q. I. Rahman, “ Inequalities for Polynomials and Entire Functions,” Archive for Rational Mechanics and Analysis, Vol. 11, 1962, pp. 34-39. doi:10.1007/BF00253927
- A. Aziz and N. A. Rather, “ Inequalities for Polynomials,” Glasnik Matematicki, Vol. 32, No. 52, 1997, pp. 39-43.
- P. D. Lax, “Proof of a Conjecture of P. Erdos on the Derivative of a Polynomial,” Bulletin of American Mathematical Society, Vol. 50, 1944, pp. 509-513. doi:10.1090/S0002-9904-1944-08177-9
- N. C. Ankeny and T. J. Rivlin, “On a Theorm of S. Bernstein,” Pacific Journal of Mathematics, Vol. 5, 1955, pp. 849-852.
- A. Aziz and N. A. Rather, “Some Compact Generalization of Zygmund-Type Inequalities for Polynomials,” Nonlinear Studies, Vol. 6, No. 2, 1999, pp. 241-255.