Abstract
Let P(z) be a polynomial of degree n which does not vanish in \(|z|<1\). Then it was proved by Hans and Lal (Anal Math 40:105–115, 2014) that
for every \(\beta \in \mathbb C\) with \(|\beta |\le 1,1\le s\le n\) and \(|z|=1.\)
The \(L^{\gamma }\) analog of the above inequality was recently given by Gulzar (Anal Math 42:339–352, 2016) who under the same hypothesis proved
where \(n_s=n(n-1)\ldots (n-s+1)\) and \(0\le \gamma <\infty \).
In this paper, we generalize this and some other related results.
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The author is extremely grateful to the anonymous referees for many valuable suggestions.
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