A generalization of Lucas' theorem to vector spaces

Neyamat Zaheer

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-10

Abstract:

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:316924

DOI: 10.1155/S0161171293000316

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