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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Main Author:	Neyamat Zaheer
Format:	Article
Language:	English
Published:	Hindawi Limited 1993-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	abstract polynomials and their pseudo-derivatives (supergeneralized) circular regions K-inner product spaces.
Online Access:	http://dx.doi.org/10.1155/S0161171293000316

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spelling	doaj-8083478d45f540558d6264668468b97f2020-11-24T22:41:36ZengHindawi LimitedInternational 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.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Neyamat Zaheer
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.
author_facet	Neyamat Zaheer
author_sort	Neyamat Zaheer
title	A generalization of Lucas' theorem to vector spaces
title_short	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_sort	generalization of lucas' theorem to vector spaces
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1993-01-01
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.
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
_version_	1725701630663327744

A generalization of Lucas' theorem to vector spaces

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