Integral mean estimates for polynomials whose zeros are within a circle
Let p(z) be a polynomial of degree n having all its zeros in |z|≤k; k≤1, then for each r>0, p>1, q>1 with p−1+q−1=1, Aziz and Ahemad (1996) recently proved that n{∫02π|p(eiθ)|rdθ}1/r≤{∫02π|1+keiθ|prdθ}1/pr{∫02π|p′(eiθ)|qrdθ}1/qr. In this paper, we extend the above inequality to the class o...
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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/S016117120100607X |
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| author | K. K. Dewan Abdullah Mir R. S. Yadav |
| author_facet | K. K. Dewan Abdullah Mir R. S. Yadav |
| author_sort | K. K. Dewan |
| collection | DOAJ |
| description | Let p(z) be a polynomial of degree n having all its zeros in |z|≤k; k≤1, then for each r>0, p>1, q>1 with p−1+q−1=1, Aziz and Ahemad (1996) recently proved that n{∫02π|p(eiθ)|rdθ}1/r≤{∫02π|1+keiθ|prdθ}1/pr{∫02π|p′(eiθ)|qrdθ}1/qr. In this paper, we extend the above inequality to the class of polynomials p(z)=anzn+∑v=μnan−vzn−v;1≤μ≤n having all its zeros in |z|≤k; k≤1 and obtain a generalization as well as a refinement of the above
result. |
| format | Article |
| id | doaj-art-042772db1cea4b9ca988930ba53b674c |
| institution | Kabale University |
| 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-042772db1cea4b9ca988930ba53b674c2025-02-03T05:47:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0128423123510.1155/S016117120100607XIntegral mean estimates for polynomials whose zeros are within a circleK. K. Dewan0Abdullah Mir1R. 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) be a polynomial of degree n having all its zeros in |z|≤k; k≤1, then for each r>0, p>1, q>1 with p−1+q−1=1, Aziz and Ahemad (1996) recently proved that n{∫02π|p(eiθ)|rdθ}1/r≤{∫02π|1+keiθ|prdθ}1/pr{∫02π|p′(eiθ)|qrdθ}1/qr. In this paper, we extend the above inequality to the class of polynomials p(z)=anzn+∑v=μnan−vzn−v;1≤μ≤n having all its zeros in |z|≤k; k≤1 and obtain a generalization as well as a refinement of the above result.http://dx.doi.org/10.1155/S016117120100607X |
| spellingShingle | K. K. Dewan Abdullah Mir R. S. Yadav Integral mean estimates for polynomials whose zeros are within a circle International Journal of Mathematics and Mathematical Sciences |
| title | Integral mean estimates for polynomials whose zeros are within a circle |
| title_full | Integral mean estimates for polynomials whose zeros are within a circle |
| title_fullStr | Integral mean estimates for polynomials whose zeros are within a circle |
| title_full_unstemmed | Integral mean estimates for polynomials whose zeros are within a circle |
| title_short | Integral mean estimates for polynomials whose zeros are within a circle |
| title_sort | integral mean estimates for polynomials whose zeros are within a circle |
| url | http://dx.doi.org/10.1155/S016117120100607X |
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