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Region of variability for functions with positive real part

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Ponnusamy S., Vasudevarao A.

Annales Polonici Mathematici

2010

tom 99

nr 3

225-245

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Ponnusamy S.

1 Vasudevarao A.

1 2010

Wyniki wyszukiwania

Region of variability for functions with positive real part