대한수학회지 (Journal of the Korean Mathematical Society)

  • 제54권1호
  • /
  • Pages.267-280
  • /
  • 2017
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ANALYTIC AND GEOMETRIC PROPERTIES OF OPEN DOOR FUNCTIONS

  • Li, Ming (Graduate School of Information Sciences Tohoku University) ;
  • Sugawa, Toshiyuki (Graduate School of Information Sciences Tohoku University)
  • 투고 : 2015.11.30
  • 발행 : 2017.01.01
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초록

In this paper, we study analytic and geometric properties of the solution q(z) to the differential equation q(z) + zq'(z)/q(z) = h(z) with the initial condition q(0) = 1 for a given analytic function h(z) on the unit disk |z| < 1 in the complex plane with h(0) = 1. In particular, we investigate the possible largest constant c > 0 such that the condition |Im [zf"(z)/f'(z)]| < c on |z| < 1 implies starlikeness of an analytic function f(z) on |z| < 1 with f(0) = f'(0) - 1 = 0.

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참고문헌

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