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Sufficiency for Gaussian hypergeometric functions to be uniformly convex

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  • Yong Chan Kim
  • S. Ponnusamy

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 .

Suggested Citation

  • Yong Chan Kim & S. Ponnusamy, 1999. "Sufficiency for Gaussian hypergeometric functions to be uniformly convex," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:457809
    DOI: 10.1155/S0161171299227652
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    Cited by:

    1. Young Jae Sim & Oh Sang Kwon, 2015. "The Pre-Schwarzian Norm Estimate for Analytic Concave Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-6, April.

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