In this paper, we consider an operator Da which maps a polynomial P(z) in to DaP(z):= np(z)+ (a-z)P'(z), where and obtain some Lγ inequalities for lucanary polynomials having zeros in /z/ 〈 k 〈 1. Ou...In this paper, we consider an operator Da which maps a polynomial P(z) in to DaP(z):= np(z)+ (a-z)P'(z), where and obtain some Lγ inequalities for lucanary polynomials having zeros in /z/ 〈 k 〈 1. Our results yields several generaliza- tions and refinements of many known results and also provide an alternative proof of a result due to Dewan et al. [7], which is independent of Laguerre's theorem.展开更多
Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P(Z)[ls for every α, β∈ C with |a|≤ 1, |β|〉 1, R 〉 r 〉 1, and s 〉 O. Our results not...Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P(Z)[ls for every α, β∈ C with |a|≤ 1, |β|〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.展开更多
文摘In this paper, we consider an operator Da which maps a polynomial P(z) in to DaP(z):= np(z)+ (a-z)P'(z), where and obtain some Lγ inequalities for lucanary polynomials having zeros in /z/ 〈 k 〈 1. Our results yields several generaliza- tions and refinements of many known results and also provide an alternative proof of a result due to Dewan et al. [7], which is independent of Laguerre's theorem.
文摘Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P(Z)[ls for every α, β∈ C with |a|≤ 1, |β|〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.