Symmetry (Oct 2018)

Third-Order Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

  • Hai-Yan Zhang,
  • Huo Tang,
  • Xiao-Meng Niu

DOI
https://doi.org/10.3390/sym10100501
Journal volume & issue
Vol. 10, no. 10
p. 501

Abstract

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Let S l * denote the class of analytic functions f in the open unit disk D = { z : | z | < 1 } normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , which is subordinate to exponential function, z f ′ ( z ) f ( z ) ≺ e z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) for this function class S l * associated with exponential function and obtain the upper bound of the determinant H 3 ( 1 ) . Meanwhile, we give two examples to illustrate the results obtained.

Keywords