JANOWSKI STARLIKENESS IN SEVERAL COMPLEX VARIABLES AND COMPLEX HILBERT SPACES

In this paper, we consider two new subclasses,S*(a, b, Bn ) and 𝒜𝒮*(a, b, Bn ), of the class of starlike mappings onBn (a, b∈ ℝ, |a− 1| <b≤a, andBn is the Euclidean unit ball in ℂ n ). The classS*(a, b, B) is then-dimensional version of Janowski class of one variable starlike functions. We obtain...

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Published inTaiwanese journal of mathematics Vol. 18; no. 4; pp. 1171 - 1184
Main Author Curt, Paula
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2014
Subjects
Complex variables
Hilbert spaces
Mathematical functions
Unit ball
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.18.2014.3917

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Summary:In this paper, we consider two new subclasses,S*(a, b, Bn ) and 𝒜𝒮*(a, b, Bn ), of the class of starlike mappings onBn (a, b∈ ℝ, |a− 1| <b≤a, andBn is the Euclidean unit ball in ℂ n ). The classS*(a, b, B) is then-dimensional version of Janowski class of one variable starlike functions. We obtain sharp growth results and upper distortion estimates for these two classes of starlike mappings. We also derive sufficient conditions for normalized holomorphic mappings (expressed in terms of their coefficient bounds) to belong to one of the classesS*(a, b, Bn ), respectively 𝒜𝒮*(a, b, Bn ). Finally, similar notions on the unit ball in a complex Hilbert space are analogously presented. 2010Mathematics Subject Classification: 32H02, 30C45. Key words and phrases: Biholomorphic mapping, Locally biholomorphic mapping, Starlike mapping, Almost starlike mapping.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.18.2014.3917