PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2020 | 74 | 1 |
Tytuł artykułu

Inequalities concerning the rate of growth of polynomials involving the polar derivative

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper contains some results for algebraic polynomials in the complex plane involving the polar derivative that are inspired by some classical results of Bernstein. Obtained results yield the polar derivative analogues of some inequalities giving estimates for the growth of derivative of lacunary polynomials.
Słowa kluczowe
Rocznik
Tom
74
Numer
1
Opis fizyczny
Daty
wydano
2020
online
2020-10-20
Twórcy
Bibliografia
  • Aziz, A., Shah, W. M., Inequalities for a polynomial and its derivative, Math. Inequal. Appl. 7 (2004), 379–391.
  • Aziz, A., Zargar, B. A., Inequalities for a polynomial and its derivative, Math. Inequal. Appl. 1 (1998), 543–550.
  • Bernstein, S., Sur l’ordre de la meilleure approximation des functions continues par des polynomes de degr´e donne, Mem. Acad. R. Belg. 4 (1912), 1–103.
  • Bernstein, S., Sur la limitation des derivees des polynomes, C. R. Acad. Sci. Paris 190 (1930), 338–341.
  • Bidkham, M., Dewan, K. K., Inequalities for a polynomial and its derivative, J. Math. Anal. Appl., 166 (1992), 319-324.
  • Chanam, B., Dewan, K. K., Inequalities for a polynomial and its derivative, J. Math. Anal. Appl. 336 (2007), 171–179.
  • Dewan, K. K., Singh, N., Mir, A., Extensions of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009), 807–815.
  • Gardner, R. B., Govil, N. K., Musukula, S. R., Rate of growth of polynomials not vanishing inside a circle, J. Inequal. Pure Appl. Math. 6 (2), Art. 53, (2005), 1–9.
  • Govil, N. K., Rahman, Q. I., Functions of exponential type not vanishing in a half plane and related polynomials, Trans. Amer. Math. Soc. 137 (1969), 501–517.
  • Lax, P. D., Proof of a conjecture of P. Erd¨os on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509–513.
  • Malik, M. A., On the derivative of a polynomial, J. London. Math. Soc. 1 (1969), 57–60.
  • Mir, A., Hussain, I., On the Erdos–Lax inequality concerning polynomials, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 1055–1062.
  • Mir, A., On an operator preserving inequalities between polynomials, Ukrainian Math. J. 69 (2018), 1234–1247.
  • Mir, A., Dar, B., On the polar derivative of a polynomial, J. Ramanujan Math. Soc., 29 (2014), 403–412.
  • Mir, A., Wani, A., Polynomials with polar derivatives, Funct. Approx. Comment. Math. 55 (2016), 139–144.
  • Mir, A., Dar, B., Inequalities concerning the rate of growth of polynomials, Afr. Mat. 27 (2016), 279–290.
  • Somsuwan, J., Nakprasit, K. N., Some bounds for the polar derivative of a polynomial, Int. J. Math. Math. Sci. (2018), Art. ID 5034607, 4 pp.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2020_74_1_67-75
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.