MMN-1344
Regions of variability for Janowski functions
Abstract
Let A∈ℂ, B∈(-1,1]. Then P[A,B] denotes the class of analytic functions p in the open unit disk with p(0)=1 such that
p(z)=((1+Aw(z))/(1+Aw(z))),
where w(0)=0 and |w(z)|<1. In this article, we find the regions of variability V(z₀,λ) for ∫₀^{z₀}p(ρ)dρ when p ranges over the class P_{λ}[A,B] defined as
P_{λ}[A,B]={p∈P[A,B]:p′(0)=(A-B)λ}
for any fixed z₀∈E and λ∈E. As a consequence the regions of variability are also illustrated graphically for different sets of parameters.
Vol. 16 (2015), No. 2, pp. 1117-1127
DOI: 10.18514/MMN.2015.1344