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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| Datum: | 2025 |
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Institute of Mathematics, NAS of Ukraine
2025
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512931403268096 |
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| author | Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. |
| author_facet | Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. |
| author_sort | Lashin, Abdel M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-01T09:34:37Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v77i1.8143 |
| first_indexed | 2026-03-24T03:36:37Z |
| format | Article |
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| id | umjimathkievua-article-8143 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:36:37Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-81432025-11-01T09:34:37Z Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. Analytic and univalent functions Horadam polynomials bi-univalent function Fekete-Szego inequalities 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. УДК 517.5 Оцінки коефіцієнтів поліномів Горадама для деяких підкласів двочленних  функцій Базілевича Запропоновано використовувати поліноми Горадама, які, як відомо, включають в себе такі потенційно корисні поліноми, як поліноми Пелла, поліноми Чебишова другого роду, поліноми Фібоначчі, поліноми Пелла–Лукаса та поліноми Лукаса. Спочатку поліноми Горадама використано для визначення нового класу двочленних функцій. Потім знайдено оцінки для коефіцієнтів нерівностей $|c_{2}|$ і $|c_3|$ та розглянуто знамениту проблему Фекете–Сеґо для функцій, що належать цьому новому класу двочленних функцій. Також наведено відповідні зв'язки наших результатів з результатами, отриманими у попередніх дослідженнях. Institute of Mathematics, NAS of Ukraine 2025-10-31 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8143 10.3842/umzh.v77i1.8143 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 1 (2025); 73 Український математичний журнал; Том 77 № 1 (2025); 73 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8143/10296 Copyright (c) 2025 Abdel Lashin, R El-ashwah, wafaa Kouta |
| spellingShingle | Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. Lashin, Abdel M. El-Ashwah, Rabha M. Kota, Wafaa Y. Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title | Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title_alt | Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title_full | Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title_fullStr | Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title_full_unstemmed | Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title_short | Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions |
| title_sort | estimations of the coefficients of horadam polynomials for certain subclasses of bi-univalent bazilevich functions |
| topic_facet | Analytic and univalent functions Horadam polynomials bi-univalent function Fekete-Szego inequalities |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8143 |
| work_keys_str_mv | AT lashinabdelm estimationsofthecoefficientsofhoradampolynomialsforcertainsubclassesofbiunivalentbazilevichfunctions AT elashwahrabham estimationsofthecoefficientsofhoradampolynomialsforcertainsubclassesofbiunivalentbazilevichfunctions AT kotawafaay estimationsofthecoefficientsofhoradampolynomialsforcertainsubclassesofbiunivalentbazilevichfunctions AT lashinabdelm estimationsofthecoefficientsofhoradampolynomialsforcertainsubclassesofbiunivalentbazilevichfunctions AT elashwahrabham estimationsofthecoefficientsofhoradampolynomialsforcertainsubclassesofbiunivalentbazilevichfunctions AT kotawafaay estimationsofthecoefficientsofhoradampolynomialsforcertainsubclassesofbiunivalentbazilevichfunctions |