Sufficiency for Gaussian hypergeometric functions to be uniformly convex

Yong Chan Kim and S. Ponnusamy

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-9

Abstract:

Let F ( a , b ; c ; z ) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰 . Let an operator I a , b ; c ( f ) be defined by [ I a , b ; c ( f ) ] ( z ) = z F ( a , b ; c ; z ) * f ( z ) . In this paper the authors identify two subfamilies of analytic functions ℱ 1 and ℱ 2 and obtain conditions on the parameters a , b , c such that f ∈ ℱ 1 implies I a , b ; c ( f ) ∈ ℱ 2 .

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:457809

DOI: 10.1155/S0161171299227652

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