Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE COEFFICIENTS OF GAMMA-STARLIKE FUNCTIONS

  • Thomas, Derek K. (Department of Mathematics Swansea University)
  • Received : 2017.02.08
  • Accepted : 2017.10.31
  • Published : 2018.01.01
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Abstract

We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions f, analytic and univalent in the unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$, and normalized so that f(0) = 0 = f'(0)-1, and satisfying Re $\left[\left(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\right)^{\gamma}\left({\frac{zf^{\prime}(z)}{f(z)}}\right)^{1-{\gamma}}\right]$ > 0.

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References

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