A new inequality for a polynomial
Let p(z)=a0+∑j=tnajzj be a polynomial of degree n, having no zeros in |z|<k, k≥1 then it has been shown that for R>1 and |z|=1, |p(Rz)−p(z)|≤(Rn−1)(1+AtBtKt+1)/(1+kt+1+AtBt(kt+1+k2t))max|z|=1|p(z)|−{1−(1+AtBtkt+1)/(1+kt+1+AtBt(kt+1+k2t))}((Rn−1)m/kn), where m=min|z|=k|p(z)|, 1≤t<n, At=(Rt−1...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006032 |
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| _version_ | 1850237701290196992 |
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| author | K. K. Dewan Harish Singh R. S. Yadav |
| author_facet | K. K. Dewan Harish Singh R. S. Yadav |
| author_sort | K. K. Dewan |
| collection | DOAJ |
| description | Let p(z)=a0+∑j=tnajzj be a polynomial of degree n, having no zeros in |z|<k, k≥1 then it has been shown that for R>1 and |z|=1, |p(Rz)−p(z)|≤(Rn−1)(1+AtBtKt+1)/(1+kt+1+AtBt(kt+1+k2t))max|z|=1|p(z)|−{1−(1+AtBtkt+1)/(1+kt+1+AtBt(kt+1+k2t))}((Rn−1)m/kn), where m=min|z|=k|p(z)|, 1≤t<n, At=(Rt−1)/(Rn−1), and Bt=|at/a0|. Our result generalizes and improves some
well-known results. |
| format | Article |
| id | doaj-art-1e1f1ed31a634f7fa36874dcaba8515c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1e1f1ed31a634f7fa36874dcaba8515c2025-08-20T02:01:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01281167968410.1155/S0161171201006032A new inequality for a polynomialK. K. Dewan0Harish Singh1R. S. Yadav2Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, IndiaDepartment of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, IndiaDepartment of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, IndiaLet p(z)=a0+∑j=tnajzj be a polynomial of degree n, having no zeros in |z|<k, k≥1 then it has been shown that for R>1 and |z|=1, |p(Rz)−p(z)|≤(Rn−1)(1+AtBtKt+1)/(1+kt+1+AtBt(kt+1+k2t))max|z|=1|p(z)|−{1−(1+AtBtkt+1)/(1+kt+1+AtBt(kt+1+k2t))}((Rn−1)m/kn), where m=min|z|=k|p(z)|, 1≤t<n, At=(Rt−1)/(Rn−1), and Bt=|at/a0|. Our result generalizes and improves some well-known results.http://dx.doi.org/10.1155/S0161171201006032 |
| spellingShingle | K. K. Dewan Harish Singh R. S. Yadav A new inequality for a polynomial International Journal of Mathematics and Mathematical Sciences |
| title | A new inequality for a polynomial |
| title_full | A new inequality for a polynomial |
| title_fullStr | A new inequality for a polynomial |
| title_full_unstemmed | A new inequality for a polynomial |
| title_short | A new inequality for a polynomial |
| title_sort | new inequality for a polynomial |
| url | http://dx.doi.org/10.1155/S0161171201006032 |
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