Univalence and convexity properties for gaussian hypergeometric functions

: Ponnusamy S., Vuorinen M.

: 2001

: Rocky Mountain Journal of Mathematics

: 31

: 1

: 327

: 352

: 26

: 0035-7596

: http://api.elsevier.com/content/abstract/scopus_id:0035531056

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.