Region of variability for functions with positive real part

• Autorzy: Saminathan Ponnusamy , Allu Vasudevarao
• Języki publikacji: EN

Abstrakty

EN

For γ ∈ ℂ such that |γ| < π/2 and 0 ≤ β < 1, let $𝓟_{γ,β}$ denote the class of all analytic functions P in the unit disk 𝔻 with P(0) = 1 and
$Re(e^{iγ}P(z)) > βcosγ$ in 𝔻.
For any fixed z₀ ∈ 𝔻 and λ ∈ 𝔻̅, we shall determine the region of variability $V_{𝓟}(z₀,λ)$ for $∫_0^{z₀} P(ζ)dζ$ when P ranges over the class
$𝓟(λ) = {P ∈ 𝓟_{γ,β} : P'(0) = 2(1-β)λe^{-iγ} cosγ}.
As a consequence, we present the region of variability for some subclasses of univalent functions. We also graphically illustrate the region of variability for several sets of parameters.

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C55: General theory of univalent and multivalent functions
• 30C80: Maximum principle; Schwarz's lemma, Lindel\"of principle, analogues and generalizations; subordination

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 99
• Numer: 3
• Strony: 225-245

Daty

wydano

2010

Twórcy

autor

Saminathan Ponnusamy

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

autor

Allu Vasudevarao

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

Identyfikatory

DOI

10.4064/ap99-3-2