Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME REMARKS OF THE CARATHÉODORY'S INEQUALITY ON THE RIGHT HALF PLANE

  • Received : 2018.11.14
  • Accepted : 2019.08.07
  • Published : 2020.01.31
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Abstract

In this paper, a boundary version of Carathéodory's inequality on the right half plane for p-valent is investigated. Let Z(s) = 1+cp (s - 1)p +cp+1 (s - 1)p+1 +⋯ be an analytic function in the right half plane with ℜZ(s) ≤ A (A > 1) for ℜs ≥ 0. We derive inequalities for the modulus of Z(s) function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of these inequalities is proved.

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References

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