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The Pre-Schwarzian Norm Estimate for Analytic Concave Functions

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  • Young Jae Sim
  • Oh Sang Kwon

Abstract

Let denote the open unit disk and let denote the class of normalized univalent functions which are analytic in . Let be the class of concave functions , which have the condition that the opening angle of at infinity is less than or equal to , . In this paper, we find a sufficient condition for the Gaussian hypergeometric functions to be in the class . And we define a class , , which is a subclass of and we find the set of variabilities for the functional for . This gives sharp upper and lower estimates for the pre-Schwarzian norm of functions in . We also give a characterization for functions in in terms of Hadamard product.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:814805
    DOI: 10.1155/2015/814805
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    References listed on IDEAS

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    1. 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.
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