Korean J. Math. Vol. 24 No. 3 (2016) pp.369-374
DOI: https://doi.org/10.11568/kjm.2016.24.3.369

Sharp hereditary convex radius of convex harmonic mappings under an integral operator

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Xingdi Chen
Jingjing Mu


In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+\overline{f_2(z)}$ under the integral operator $I_{f}(z)=\int_{0}^{z}\frac{f_1(u)}{u}du+\overline{\int_{0}^z\frac{f_2(u)}{u}}$ and obtain the sharp constant $\frac{4\sqrt{6}-\sqrt{15}}{9}$, which generalized the result corresponding to the class of analytic functions given by Nash.

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Supporting Agencies

This work was supported by NNSF of China (11471128) the Natural Science Foundation of Fujian Province of China (2014J01013) NCETFJ Fund (2012FJ-NCET-ZR05) Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao


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