대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권1호
  • /
  • Pages.75-81
  • /
  • 2014
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A SHARP SCHWARZ AND CARATHÉODORY INEQUALITY ON THE BOUNDARY

  • 투고 : 2013.05.03
  • 발행 : 2014.01.31
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초록

In this paper, a boundary version of the Schwarz and Carath$\acute{e}$odory inequality are investigated. New inequalities of the Carath$\acute{e}$odory's inequality and Schwarz lemma at boundary are obtained by taking into account zeros of f(z) function which are different from zero. The sharpness of these inequalities is also proved.

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참고문헌

  1. G. Kresin and V. Maz'ya, Sharp Real-Part Theorems: A Unified Approach, Translated from the Russian and edited by T. Shaposhnikova. Lecture Notes in Mathematics, 1903. Springer, Berlin, 2007.
  2. A. I. Markushevich, Theory of Functions of a Complex Variable. Vol. I, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1965.
  3. R. Osserman, A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc. 128 (2000), no. 12, 3513-3517. https://doi.org/10.1090/S0002-9939-00-05463-0
  4. Ch. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.