Some inequalities for polynomials with a multiple zero at origin Article Swipe
M. Y. Mir
,
Sirish L. Shah
,
Wali Mohammad Shah
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5269/bspm.68376
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5269/bspm.68376
If $P(z)$ is a polynomial of degree $n$ with origin as a zero of some multiplicity, then the estimate for $|P'(z)|$ in terms of $|P(z)|$ on $| z|=1$, when all other zeros of $P(z)$ lie in $|z|\le k,~ k\le 1$, is known [A. Aziz and W. M. Shah, \textit{Math. Inequal. Appl.,}~\textbf{7}(3)(2004),~379-391]. In this paper we prove some results in case $P(z)$ has a zero of multiplicity $s\ge 0$ at origin and all other zeros in $|z|\ge k, k\ge 1,$ as well as on $|z|=k , k\leq1$. We also consider s-fold lacunary polynomials of degree $n,$ by which we generalize some earlier well known results.
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- article
- Language
- en
- Landing Page
- https://doi.org/10.5269/bspm.68376
- https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/download/68376/751375159491/
- OA Status
- diamond
- References
- 9
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4412571101
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https://openalex.org/W4412571101Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5269/bspm.68376Digital Object Identifier
- Title
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Some inequalities for polynomials with a multiple zero at originWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-03-24Full publication date if available
- Authors
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M. Y. Mir, Sirish L. Shah, Wali Mohammad ShahList of authors in order
- Landing page
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https://doi.org/10.5269/bspm.68376Publisher landing page
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https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/download/68376/751375159491/Direct link to full text PDF
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diamondOpen access status per OpenAlex
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https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/download/68376/751375159491/Direct OA link when available
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Zero (linguistics), Mathematics, Inequality, Pure mathematics, Mathematical analysis, Philosophy, LinguisticsTop concepts (fields/topics) attached by OpenAlex
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