Generalized Bounded Turning Functions Connected with Gregory Coefficients.

In this research article, we introduce new family R G of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for the functions belonging to this newly defined family, demonstrating their sharpness. Furthermore, we find the third Hankel determinant for functions in the class R G . Moreover, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the under-considered class R G are estimated. [ABSTRACT FROM AUTHOR]