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In this paper we introduced the class $\mathcal{S}_{G}^{\ast }$ of analyticfunctions which is related with starlike functions and generating function ofGregory coefficients. By using bounds on some coefficient functionals for thefamily of functions with positive real part, we obtain for functions in theclass $\mathcal{S}_{G}^{\ast }$ several sharp coefficient bounds on the firstsix coeffcients and also further sharp bounds on the corresponding Hankeldeterminants.

Sharp coefficients bounds for Starlike functions associated with Gregory coefficients