A new inequality for a polynomial. (13th December 2001) - Dewan, K. K.; Singh, Harish; Yadav, R. S.
Abstract : Letp ( z ) = a 0 + ∑ j = t n a j z j be a polynomial of degreen, having no zeros in| z | < k, k ≥ 1 then it has been shown that forR > 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 ), wherem = min | z | = k | p ( z ) |, 1 ≤ t < n, A t = ( R t − 1 ) / ( R n − 1 ), andB t = | a t / a 0 | . Our result generalizes and improves some well-known results.