Abstract
In the present paper, we obtain the estimates for the first two initial Taylor-Maclaurin coefficients and for the upper bounds of the Fekete-Szegö functional for new subclasses of the class \(\Sigma \) of normalized analytic and bi-univalent functions, which are defined here with the aid of the Nephroid function. We also determine upper bounds of the functional \(\left| a_{2}a_{4}-a_{3}^{2}\right| \) for the functions that belong to these classes. A related open problem as well some potential directions for further researches are posed in the concluding section.
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Srivastava, H.M., Murugusundaramoorthy, G. & Bulboacă, T. The second Hankel determinant for subclasses of Bi-univalent functions associated with a nephroid domain. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 145 (2022). https://doi.org/10.1007/s13398-022-01286-6
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DOI: https://doi.org/10.1007/s13398-022-01286-6
Keywords
- Analytic and univalent functions
- Starlike and convex functions
- Bi-Univalent functions
- Strongly bi-starlike functions
- Coefficient bounds
- Subordination
- Fekete-Szegö inequalities
- Hankel determinant