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In the present paper with the aid of subordination, the authors introduce two subclasses of analytic functions denoted by S α , β (λ) (α , β , λ ∈ R , α < 1 , β > 1 , λ ≥ 0) and G (λ) defined in the open unit disk D : = { z ∈ C : | z | < 1 } . These subclasses are defined through a certain univalent function S α , β and the generating function of the Gregory coefficients G (λ) . We determine upper bounds of the initial coefficients, Fekete–Szeg o ¨ functional, Hankel determinant of second order, logarithmic coefficients and inverse coefficients of the functions belongs to these subclasses. Some of the corollaries of the main results are also pointed out. [ABSTRACT FROM AUTHOR]

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]

In this paper we introduced the class S G ∗ of analytic functions which is related with starlike functions and generating function of Gregory coefficients. By using bounds on some coefficient functionals for the family of functions with positive real part, we obtain several sharp coefficient bounds on the first six coefficients and also further bounds on the corresponding Hankel determinants for functions in the class S G ∗ . Additionally, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the considered class S G ∗ were estimated. [ABSTRACT FROM AUTHOR]