Region of variability for functions with positive real part

Saminathan Ponnusamy; Allu Vasudevarao

Annales Polonici Mathematici, Tome 98 (2010), p. 225-245 / Harvested from The Polish Digital Mathematics Library

Résumé

For γ ∈ ℂ such that |γ| < π/2 and 0 ≤ β < 1, let $_{γ, β}$ denote the class of all analytic functions P in the unit disk with P(0) = 1 and $R e (e^{i γ} P (z)) > β c o s γ$ in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability $V_{} (z ₀, λ)$ for $\int_{0}^{z ₀} P (ζ) d ζ$ when P ranges over the class $(λ) = P \in_{γ, β} : P^{'} (0) = 2 (1 - β) λ e^{- i γ} c o s γ .$ 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.

Publié le : 2010-01-01

Zbl 1209.30007

EUDML-ID : urn:eudml:doc:280770

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     author = {Saminathan Ponnusamy and Allu Vasudevarao},
     title = {Region of variability for functions with positive real part},
     journal = {Annales Polonici Mathematici},
     volume = {98},
     year = {2010},
     pages = {225-245},
     zbl = {1209.30007},
     language = {en},
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Saminathan Ponnusamy; Allu Vasudevarao. Region of variability for functions with positive real part. Annales Polonici Mathematici, Tome 98 (2010) pp. 225-245. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-3-2/