Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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PRODUCT AND CONVOLUTION OF CERTAIN UNIVALENT FUNCTIONS

  • Received : 2016.05.30
  • Accepted : 2016.10.24
  • Published : 2016.12.25
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Abstract

For $f_i$ belonging to various subclasses of univalent functions, we investigate the product given by $h(z)=z{\prod_{i=1}^{n}}(f_i(z)/z)^{{\gamma}_i}$.The largest radius ${\rho}$ is determined such that $h({\rho}z)/{\rho}$ is starlike of order ${\beta}$, $0{\leq}{\beta}$ < 1 or to belong to other subclasses of univalent functions. We also determine the sharp radius of starlikeness of order ${\beta}$and other radius for the convolution f*g of two starlike functions f, g.

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References

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