A new inequality for a polynomial

K. K. Dewan, Harish Singh and R. S. Yadav

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 28, 1-6

Abstract:

Let p ( z ) = a 0 + ∑ j = t n a j z j be a polynomial of degree n , having no zeros in | z | < k , k ≥ 1 then it has been shown that for R > 1 and | z | = 1 , | p ( R z ) − p ( z ) | ≤ ( R n − 1 ) ( 1 + A t B t K t + 1 ) / ( 1 + k t + 1 + A t B t ( k t + 1 + k 2 t ) ) max | z | = 1 | p ( z ) | − { 1 − ( 1 + A t B t k t + 1 ) / ( 1 + k t + 1 + A t B t ( k t + 1 + k 2 t ) ) } ( ( R n − 1 ) m / k n ) , where m = min | z | = k | p ( z ) | , 1 ≤ t < n , A t = ( R t − 1 ) / ( R n − 1 ) , and B t = | a t / a 0 | . Our result generalizes and improves some well-known results.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:634218

DOI: 10.1155/S0161171201006032

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