The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ON A CLASS OF ANALYTIC FUNCTION RELATED TO SCHWARZ LEMMA

  • Received : 2021.11.28
  • Accepted : 2022.01.17
  • Published : 2022.02.28
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Abstract

In this paper, we plan to introduce the class of the analytic functions called 𝒫 (b) and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient c2 in the expansion of f(z) = z+c2z2+… belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of f(z) function at the boundary point 𝛼 with f'(𝛼) = 1 - b, b ∈ ℂ, by taking into account their first nonzero two Maclaurin coefficients.

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References

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