Abstract
Let p(z) be a polynomial of degree n with zero of multiplicity s at the origin and the remaining zeros in \(|z|\ge k\) or in \(|z|\le k\), \(k>0\). In this paper, first we obtain inequalities about the dependence of |p(Rz)| on |p(rz)|, where \(|z|=1\), for \(r^2\le Rr\le k^2\) or \(k^2\le Rr \le R^2\). Further, another similar inequality for the class of polynomials having all zeros in \(|z|\ge k\), \(k>0\) is also proved for \(0<r\le R\le k\). Our results improve as well as generalize certain well-known polynomial inequalities.
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Communicated by Ali Abkar.
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Chanam, B., Devi, K.B., Krishnadas, K. et al. On Maximum Modulus of Polynomials with Restricted Zeros. Bull. Iran. Math. Soc. 48, 1325–1338 (2022). https://doi.org/10.1007/s41980-021-00575-x
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DOI: https://doi.org/10.1007/s41980-021-00575-x