On the derivative of a polynomial and Chebyshev approximation
نویسندگان
چکیده
منابع مشابه
extensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولOn the polar derivative of a polynomial
For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...
متن کاملOn the $s^{th}$ derivative of a polynomial
For every $1leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.
متن کاملOn the $s^{th}$ Derivative of a Polynomial-II
The paper presents an $L^{r}-$ analogue of an inequality regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.
متن کاملon the polar derivative of a polynomial
for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1953
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1953-0060640-x