Abstract
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.
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The authors would like to express their sincere thanks to the esteemed Referee(s) for their careful readings, valuable suggestions and comments, which helped to improve the presentation of the paper.
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Vamshee Krishna, D., RamReddy, T. Coefficient inequality for parabolic starlike functions of order alpha. Afr. Mat. 27, 121–132 (2016). https://doi.org/10.1007/s13370-015-0322-y
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DOI: https://doi.org/10.1007/s13370-015-0322-y
Keywords
- Analytic function
- Parabolic starlike function
- Uniformly convex function
- Upper bound
- Second Hankel functional
- Positive real function
- Subordination
- Toeplitz determinants