A1 Refereed original research article in a scientific journal
Univalence and convexity properties for gaussian hypergeometric functions
Authors: Ponnusamy S., Vuorinen M.
Publication year: 2001
Journal: Rocky Mountain Journal of Mathematics
Journal name in source: Rocky Mountain Journal of Mathematics
Volume: 31
Issue: 1
First page : 327
Last page: 352
Number of pages: 26
ISSN: 0035-7596
Web address : http://api.elsevier.com/content/abstract/scopus_id:0035531056
Abstract
Let A = {f : Δ → C|f(z) = z + ΣΑz}. We study sufficient/necessary conditions, in terms of the coefficients Α, for a function f ∈ A to be member of well-known subclasses of the class S of univalent functions. Examples of these subclasses include starlike, convex, close-to-convex functions. In particular, functions of the form zF (a, b; c; z) are considered, where F(a, b; c; z) is the hypergeometric function. Key words and phrases. Gaussian hypergeometric functions, univalent, convex and starlike functions.
Let A = {f : Δ → C|f(z) = z + ΣΑz}. We study sufficient/necessary conditions, in terms of the coefficients Α, for a function f ∈ A to be member of well-known subclasses of the class S of univalent functions. Examples of these subclasses include starlike, convex, close-to-convex functions. In particular, functions of the form zF (a, b; c; z) are considered, where F(a, b; c; z) is the hypergeometric function. Key words and phrases. Gaussian hypergeometric functions, univalent, convex and starlike functions.
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