Region of variability for spiral-like functions with respect to a boundary point

• Autorzy: S. Ponnusamy , A. Vasudevarao , M. Vuorinen
• Języki publikacji: EN

Abstrakty

EN

For μ ∈ ℂ such that Re μ > 0 let $ℱ_{μ}$ denote the class of all non-vanishing analytic functions f in the unit disk 𝔻 with f(0) = 1 and
$Re(2π/μ zf'(z)/f(z) + (1+z)/(1-z)) > 0$ in 𝔻.
For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ 𝔻̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class
$ℱ_{μ}(λ) = {f ∈ ℱ_{μ}: f'(0) = (μ/π)(λ - 1) and f''(0) = (μ/π)(a(1-|λ|²) + (μ/π)(λ-1)² - (1-λ²))}$.
In the final section we graphically illustrate the region of variability for several sets of parameters.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 116
• Numer: 1
• Strony: 31-46

Daty

wydano

2009

Twórcy

autor

S. Ponnusamy

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

autor

A. Vasudevarao

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

autor

M. Vuorinen

• Department of Mathematics, FIN-20014 University of Turku, Finland

Identyfikatory

DOI

10.4064/cm116-1-3