Lp-inequalities for the polar derivative of a lacunary-type polynomial
نویسندگان
چکیده
In this paper, we extend an inequality concerning the polar derivative of a polynomial in Lp-norm to class lacunary polynomials and thereby obtain bound that depends on some coefficients as well.
منابع مشابه
extensions of some polynomial inequalities to the polar derivative
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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|=...
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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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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: ??????? ?????-?????????????? ????????????
سال: 2021
ISSN: ['1811-9905', '2542-2251']
DOI: https://doi.org/10.21638/spbu01.2021.311