A generalization of Lucas' theorem to vector spaces
The classical Lucas' theorem on critical points of complex-valued polynomials has been generalized (cf. [1]) to vector-valued polynomials defined on K-inner product spaces. In the present paper, we obtain a generalization of Lucas' theorem to vector-valued abstract polynomials defined on v...
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171293000316 |
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| _version_ | 1841524639104237568 |
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| author | Neyamat Zaheer |
| author_facet | Neyamat Zaheer |
| author_sort | Neyamat Zaheer |
| collection | DOAJ |
| description | The classical Lucas' theorem on critical points of complex-valued polynomials has been generalized
(cf. [1]) to vector-valued polynomials defined on K-inner product spaces. In the present paper, we obtain
a generalization of Lucas' theorem to vector-valued abstract polynomials defined on vector spaces, in
general, which includes the above result of the author [1] in K-inner product spaces. Our main theorem
also deduces a well-known result due to Marden on linear combinations of polynomial and its derivative.
At the end, we discuss some examples in support of certain claims. |
| format | Article |
| id | doaj-art-8083478d45f540558d6264668468b97f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8083478d45f540558d6264668468b97f2025-02-03T05:47:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116226727610.1155/S0161171293000316A generalization of Lucas' theorem to vector spacesNeyamat Zaheer0Mathematics Department, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThe classical Lucas' theorem on critical points of complex-valued polynomials has been generalized (cf. [1]) to vector-valued polynomials defined on K-inner product spaces. In the present paper, we obtain a generalization of Lucas' theorem to vector-valued abstract polynomials defined on vector spaces, in general, which includes the above result of the author [1] in K-inner product spaces. Our main theorem also deduces a well-known result due to Marden on linear combinations of polynomial and its derivative. At the end, we discuss some examples in support of certain claims.http://dx.doi.org/10.1155/S0161171293000316abstract polynomials and their pseudo-derivatives(supergeneralized) circular regionsK-inner product spaces. |
| spellingShingle | Neyamat Zaheer A generalization of Lucas' theorem to vector spaces International Journal of Mathematics and Mathematical Sciences abstract polynomials and their pseudo-derivatives (supergeneralized) circular regions K-inner product spaces. |
| title | A generalization of Lucas' theorem to vector spaces |
| title_full | A generalization of Lucas' theorem to vector spaces |
| title_fullStr | A generalization of Lucas' theorem to vector spaces |
| title_full_unstemmed | A generalization of Lucas' theorem to vector spaces |
| title_short | A generalization of Lucas' theorem to vector spaces |
| title_sort | generalization of lucas theorem to vector spaces |
| topic | abstract polynomials and their pseudo-derivatives (supergeneralized) circular regions K-inner product spaces. |
| url | http://dx.doi.org/10.1155/S0161171293000316 |
| work_keys_str_mv | AT neyamatzaheer ageneralizationoflucastheoremtovectorspaces AT neyamatzaheer generalizationoflucastheoremtovectorspaces |