L_q Norm inequalities for the polar derivative of a polynomial
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 اولInequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin
Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$, let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$. Dewan et al proved that if $p(z)$ has all its zeros in $|z| leq k, (kleq 1),$ with $s$-fold zeros at the origin then for every $alphainmathbb{C}$ with $|alpha|geq k$, begin{align*} max_{|z|=...
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 کاملInequalities for the Polar Derivative of a Polynomial
In this paper we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Shah [An integral mean estimate for polynomial, Indian J. Pure Appl. Math. 28 (1997) 1413–1419] and Gardner, Govil and Weems [Some result concerning rate of growth of polynomials, East J. Apporox. 10(2004) 30...
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...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2008
ISSN: 1331-4343
DOI: 10.7153/mia-11-20