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On the conjecture of Hayami and Owa concerning the class ℛ(α)

  • Paweł Zaprawa ORCID logo EMAIL logo
Published/Copyright: May 19, 2017

Abstract

In the paper we discuss the functional Φf(μ)a2a4-μa32 for functions in the class (α), α[0,1). This class consists of analytic functions which satisfy the condition Ref(z)>α for all z in the unit disk Δ. We show that the conjecture of Hayami and Owa [1], that is, |Φf(μ)|(1-α)2max{12-49μ,49μ} for all f(α) and μ, is false. Moreover, we find estimates of |Φf(μ)| that improve the results obtained by Hayami and Owa.

MSC 2010: 30C50; 30C45

References

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Received: 2016-10-16
Accepted: 2017-4-24
Published Online: 2017-5-19
Published in Print: 2017-6-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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