Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions
UDC 517.5 We propose to  use  the Horadam polynomials, which are known to include some   potentially useful polynomials, such as the Pell polynomials, the Chebyshev polynomials of the second kind, the Fibonacci polynomials, the Pell–Lucas polynomials, and the L...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8143 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We propose to  use  the Horadam polynomials, which are known to include some   potentially useful polynomials, such as the Pell polynomials, the Chebyshev polynomials of the second kind, the Fibonacci polynomials, the Pell–Lucas polynomials, and the Lucas polynomials.  First, we use the Horadam polynomials to define a new class of bi-univalent functions.  Then we establish estimates for the coefficients of inequalities $|c_{2}|$ and $|c_3|$ and consider the celebrated Fekete–Szegö problem for functions that belong to this new class of  bi-univalent functions.  We also provide relevant connections of our results with the results obtained in earlier investigations. |
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| DOI: | 10.3842/umzh.v77i1.8143 |