In this paper, we consider the class of polynomials P（z）= anz^n＋ ∑vn=μan-vz^n-v,1≤μ≤n , having all zeros in ｜z｜≤k, k ≤1 and thereby present an alternative proof, independent of Laguerre＇s theorem, of an...In this paper, we consider the class of polynomials P（z）= anz^n＋ ∑vn=μan-vz^n-v,1≤μ≤n , having all zeros in ｜z｜≤k, k ≤1 and thereby present an alternative proof, independent of Laguerre＇s theorem, of an inequality concerning the polar derivative of a polynomial.展开更多
Let P（z） be a polynomial of degree n, having all its zeros in ｜z｜≤ 1. In this paper, we estimate kth polar derivative of P（z） on ｜z｜ = 1 and thereby obtain compact generalizations of some known results which ...Let P（z） be a polynomial of degree n, having all its zeros in ｜z｜≤ 1. In this paper, we estimate kth polar derivative of P（z） on ｜z｜ = 1 and thereby obtain compact generalizations of some known results which among other things yields a refinement of a result due to Paul Tura＇n.展开更多
基金supported by the University of Kashmir vide No: F (Seed Money Grant) RES/KU/13
文摘In this paper, we consider the class of polynomials P（z）= anz^n＋ ∑vn=μan-vz^n-v,1≤μ≤n , having all zeros in ｜z｜≤k, k ≤1 and thereby present an alternative proof, independent of Laguerre＇s theorem, of an inequality concerning the polar derivative of a polynomial.
文摘Let P（z） be a polynomial of degree n, having all its zeros in ｜z｜≤ 1. In this paper, we estimate kth polar derivative of P（z） on ｜z｜ = 1 and thereby obtain compact generalizations of some known results which among other things yields a refinement of a result due to Paul Tura＇n.
