대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권6호
  • /
  • Pages.1783-1789
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  • 2018
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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LOGHARMONIC MAPPINGS WITH TYPICALLY REAL ANALYTIC COMPONENTS

  • AbdulHadi, Zayid (Department of Mathematics American University of Sharjah) ;
  • Alarifi, Najla M. (Department of Mathematics Imam Abdulrahman Bin Faisal University) ;
  • Ali, Rosihan M. (School of Mathematical Sciences Universiti Sains Malaysia)
  • 투고 : 2017.12.11
  • 심사 : 2018.05.16
  • 발행 : 2018.11.30
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초록

This paper treats the class of normalized logharmonic mappings $f(z)=zh(z){\overline{g(z)}}$ in the unit disk satisfying ${\varphi}(z)=zh(z)g(z)$ is analytically typically real. Every such mapping f admits an integral representation in terms of its second dilatation function and a function of positive real part with real coefficients. The radius of starlikeness and an upper estimate for arclength are obtained. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when its second dilatation has real coefficients.

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과제정보

연구 과제 주관 기관 : Universiti Sains Malaysia

참고문헌

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