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 |
| Published: |
Hindawi Limited
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000316 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |