Abstract
In this paper, we introduced the class $$\mathcal {S}_{T}^{*}(\lambda )$$ of analytic functions which is related to starlike functions and generating function of generalized telephone numbers. By using bounds on some coefficient functionals for the family of functions with positive real part, we obtain for functions in the class $$\mathcal {S}_{T}^{*}(\lambda )$$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants.
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