Region of variability for functions with positive real part

Saminathan Ponnusamy, and Allu Vasudevarao. "Region of variability for functions with positive real part." Annales Polonici Mathematici 99.3 (2010): 225-245. <http://eudml.org/doc/280770>.

@article{SaminathanPonnusamy2010,
abstract = {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 $Re(e^\{iγ\}P(z)) > βcosγ$ in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability $V_\{\}(z₀,λ)$ for $∫_0^\{z₀\} P(ζ)dζ$ when P ranges over the class $(λ) = \{P ∈ _\{γ,β\} : P^\{\prime \}(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.},
author = {Saminathan Ponnusamy, Allu Vasudevarao},
journal = {Annales Polonici Mathematici},
keywords = {univalent function; starlike function; convex function; convolution; variability region},
language = {eng},
number = {3},
pages = {225-245},
title = {Region of variability for functions with positive real part},
url = {http://eudml.org/doc/280770},
volume = {99},
year = {2010},
}

TY - JOUR
AU - Saminathan Ponnusamy
AU - Allu Vasudevarao
TI - Region of variability for functions with positive real part
JO - Annales Polonici Mathematici
PY - 2010
VL - 99
IS - 3
SP - 225
EP - 245
AB - 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 $Re(e^{iγ}P(z)) > βcosγ$ in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability $V_{}(z₀,λ)$ for $∫_0^{z₀} P(ζ)dζ$ when P ranges over the class $(λ) = {P ∈ _{γ,β} : P^{\prime }(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.
LA - eng
KW - univalent function; starlike function; convex function; convolution; variability region
UR - http://eudml.org/doc/280770
ER -