Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SHARP HEREDITARY CONVEX RADIUS OF CONVEX HARMONIC MAPPINGS UNDER AN INTEGRAL OPERATOR

  • Received : 2015.10.10
  • Accepted : 2016.07.28
  • Published : 2016.09.30
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Abstract

In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+{\bar{f_x(z)}}$ under the integral operator $I_f(z)={\int_{o}^{z}}{\frac{f_1(u)}{u}}du+{\bar{{\int_{o}^{z}}{\frac{f_x(u)}{u}}}}$ and obtain the sharp constant ${\frac{{\sqrt[4]{6}}-{\sqrt[]{15}}}{9}}$, which generalized the result corresponding to the class of analytic functions given by Nash.

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References

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