Some Inequalities for the Derivative of Polynomials
If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p′z≤n/2Mα2+Mα+π21/2, where Mα=max1≤k≤npeiα+2kπ/n. In this paper, we consider a class of polynomial Pnμ of degree n, defined as pz=a0+∑υ=μnaυzυ and present certain generalizations of above inequality...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/160485 |
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| author | Sunil Hans Dinesh Tripathi Babita Tyagi |
| author_facet | Sunil Hans Dinesh Tripathi Babita Tyagi |
| author_sort | Sunil Hans |
| collection | DOAJ |
| description | If pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p′z≤n/2Mα2+Mα+π21/2, where Mα=max1≤k≤npeiα+2kπ/n. In this paper, we consider a class of polynomial Pnμ of degree n, defined as pz=a0+∑υ=μnaυzυ and present certain generalizations of above inequality and some other well-known results. |
| format | Article |
| id | doaj-art-624ce9f67635419e9f6d6d5882103986 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-624ce9f67635419e9f6d6d58821039862025-02-03T01:25:07ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/160485160485Some Inequalities for the Derivative of PolynomialsSunil Hans0Dinesh Tripathi1Babita Tyagi2Department of Applied Sciences, School of Engineering and Technology, ITM University, Gurgaon 122017, IndiaDepartment of Mathematics, Manav Rachna College of Engineering, Faridabad 121004, IndiaDepartment of Mathematics, School of Basic and Applied Sciences, Galgotias University, Greater Noida 201306, IndiaIf pz=∑υ=0ncυzυ is a polynomial of degree n, having no zeros in z<1, then Aziz (1989) proved maxz=1p′z≤n/2Mα2+Mα+π21/2, where Mα=max1≤k≤npeiα+2kπ/n. In this paper, we consider a class of polynomial Pnμ of degree n, defined as pz=a0+∑υ=μnaυzυ and present certain generalizations of above inequality and some other well-known results.http://dx.doi.org/10.1155/2014/160485 |
| spellingShingle | Sunil Hans Dinesh Tripathi Babita Tyagi Some Inequalities for the Derivative of Polynomials Journal of Mathematics |
| title | Some Inequalities for the Derivative of Polynomials |
| title_full | Some Inequalities for the Derivative of Polynomials |
| title_fullStr | Some Inequalities for the Derivative of Polynomials |
| title_full_unstemmed | Some Inequalities for the Derivative of Polynomials |
| title_short | Some Inequalities for the Derivative of Polynomials |
| title_sort | some inequalities for the derivative of polynomials |
| url | http://dx.doi.org/10.1155/2014/160485 |
| work_keys_str_mv | AT sunilhans someinequalitiesforthederivativeofpolynomials AT dineshtripathi someinequalitiesforthederivativeofpolynomials AT babitatyagi someinequalitiesforthederivativeofpolynomials |