• 제목/요약/키워드: fully starlike harmonic mappings

검색결과 1건 처리시간 0.017초

RADIUS OF FULLY STARLIKENESS AND FULLY CONVEXITY OF HARMONIC LINEAR DIFFERENTIAL OPERATOR

  • Liu, ZhiHong;Ponnusamy, Saminathan
    • 대한수학회보
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    • 제55권3호
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    • pp.819-835
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    • 2018
  • Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].