On Visser's inequality concerning coefficient estimates for a polynomial

2024/11/29 by Gulzar, Suhail, Rather, N. A., Wani, M. S
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.19831

Abstract

If P(z)=∑_j=0ⁿa_jz^j is a polynomial of degree n having no zero in |z|<1, then it was recently proved that for every p∈[0,+∞] and s=0,1,…,n-1, ‖a_nz+\fraca_s\binomns‖_p≤ \frac‖z+δ_0s‖_p‖1+z‖_p‖P‖_p, where δ_0s is the Kronecker delta. In this paper, we consider the class of polynomials having no zero in |z|<ρ, ρ≥ 1 and obtain some generalizations of above inequality.

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