2009/03/05 by M. Ahmadi Baseri, Baseri, M. Ahmadi, M. Bidkham +3
Mathematics · #30A06 #30A64 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30A06 #msc:30A64
paper · pdf · doi:10.48550/arxiv.0903.1041
11 pages
arxiv created 2009/03/05 · arxiv updated 2009/12/01
Let P(z) be a polynomial of degree n≥ 1. In this paper we define an operator B, as following, B[P(z)]:=λ0 P(z)+λ1 ((nz)/(2)) (P'(z))/(1!)+λ2 ((nz)/(2))2 (P''(z))/(2!), where λ0,λ1 and λ2 are such that all the zeros of u(z)=λ0 +c(n,1)λ1 z+c(n,2) λ2 z2 lie in half plane |z|≤ |z-(n)/(2)| and obtain a new generalization of some well-known results.