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Third Hankel determinants for two classes of analytic functions with real coefficients

  • Young Jae Sim ORCID logo and Paweł Zaprawa ORCID logo EMAIL logo
From the journal Forum Mathematicum

Abstract

In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H2,2 or H3,1 over different subclasses of 𝒮. Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 of typically real functions. The second object of our interest is 𝒦(i), the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.

MSC 2010: 30C50

Communicated by Shigeharu Takayama


Award Identifier / Grant number: 030/RID/2018/19

Funding statement: The project/research was financed in the framework of the project Lublin University of Technology – Regional Excellence Initiative, funded by the Polish Ministry of Science and Higher Education (contract no. 030/RID/2018/19).

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Received: 2021-01-14
Published Online: 2021-06-30
Published in Print: 2021-07-01

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