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A generalization of Lucas' theorem to vector spaces

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  • Neyamat Zaheer

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.

Suggested Citation

  • Neyamat Zaheer, 1993. "A generalization of Lucas' theorem to vector spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:316924
    DOI: 10.1155/S0161171293000316
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