Sharp coefficients bounds for Starlike functions associated with Gregory coefficients

Abstract

In this paper we introduced the class SG* of analytic functions which is related with starlike functions and generating functionof 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 coeffcients and also further sharp bounds on the corresponding Hankel determinants for functions in the class SG*. Additionally, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the considered class SG* were estimated. Mathematics Subject Classification (2010). Priminary 30C45; Secondary 30C50, 30C80.