Abstract
In this paper, two subclasses of close-to-star functions and two subclasses of close-to-convex functions are studied. By using the coefficient estimates of the known Caratheodory function classes, the upper bounds of the Zalcman functional $${J}_{3,4}$$ , Hankel determinant $${{H}_{2}}(3)$$ and Toeplitz determinant of given function classes are estimated. Some sharp results are obtained.
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