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Abstrakty
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.
$Re(e^{iγ}P(z)) > βcosγ$ 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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
225-245
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India
autor
- Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-3-2