Improvement on Hankel determinant bounds for specific holomorphic functions
In recent years, researchers have extensively investigated the Hankel determinant, which consists of coefficients appearing in a holomorphic function's Taylor-Maclaurin series. Hankel matrices are widely used in Markov processes, non-stationary signals, and other mathematical disciplines. The aim of the current research article is to first improve the bounds of coefficient-related problems by employing the well-known Carath & eacute;odory function. The problems that we are going to improve were obtained by Tang et al. The sharp estimates of the most difficult problem of geometric function theory known as the third-order Hankel determinant are also contributed here. Zalcman and Fekete-Szeg & ouml; inequalities are also studied here for the defined family of holomorphic functions.
In this article, we applied the optimal auxiliary function method, which is a newly developed semi-numerical method widely used for complicated nonlinear partial differential equations in many…
In recent years, researchers have extensively investigated the Hankel determinant, which consists of coefficients appearing in a holomorphic function's Taylor-Maclaurin series. Hankel matrices are…
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