Journal
AIMS MATHEMATICS
Volume 8, Issue 11, Pages 27396-27413Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.20231402
Keywords
holomorphic functions; Hankel determinant; subordination; hyperbolic function
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The work presented in this article aims to establish a new subfamily of holomorphic functions and investigate the estimate problems of their Hankel determinants and logarithmic coefficients.
The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given.
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