Coefficient inequality for parabolic starlike functions of order alpha

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The aim of this paper is to obtain a sharp upper bound to the second Hankel determinant \(|a_{2}a_{4}-a_{3}^{2}|\) for the function \(f\) when it belongs to the class of parabolic starlike functions of order \(\alpha (0\le \alpha <1).\) Further, an upper bound for the inverse function of \(f\) to the non-linear functional \(|t_{2}t_{4}-t_{3}^{2}|\) was determined when it belongs to the same class of functions, using Toeplitz determinants.