Some remarks for analytic functions related to Fibonacci polynomials and their applications
UDC 517.5 We study the relationship between certain Fibonacci polynomials and the Schwarz lemma within the framework of the complex analysis and control engineering. The Fibonacci polynomials are traditionally associated with combinatorial mathematics and recursive sequences. At the same time, they...
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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9079 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513379260563456 |
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| author | Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba |
| author_facet | Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba |
| author_sort | Düzenli, Timur |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:35:21Z |
| description | UDC 517.5
We study the relationship between certain Fibonacci polynomials and the Schwarz lemma within the framework of the complex analysis and control engineering. The Fibonacci polynomials are traditionally associated with combinatorial mathematics and recursive sequences. At the same time, they also play a significant role in the power series expansions of analytic functions. We present a version of the Schwarz lemma based on the first Fibonacci polynomial. By considering the boundary version of the Schwarz lemma, we deduce new inequalities that provide deeper insights into the relationship between these two mathematical concepts. Beyond their theoretical significance, we also present practical implications of our results. Specifically, we show that the deduced results can be applied to get marginally stable discrete-time transfer functions in digital control systems. |
| doi_str_mv | 10.3842/umzh.v77i11.9079 |
| first_indexed | 2026-03-24T03:43:45Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9079 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:43:45Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-90792026-03-21T13:35:21Z Some remarks for analytic functions related to Fibonacci polynomials and their applications Some remarks for analytic functions related to Fibonacci polynomials and their applications Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba Fibonacci polynomials Schwarz lemma Principle of Subordination 30C80 UDC 517.5 We study the relationship between certain Fibonacci polynomials and the Schwarz lemma within the framework of the complex analysis and control engineering. The Fibonacci polynomials are traditionally associated with combinatorial mathematics and recursive sequences. At the same time, they also play a significant role in the power series expansions of analytic functions. We present a version of the Schwarz lemma based on the first Fibonacci polynomial. By considering the boundary version of the Schwarz lemma, we deduce new inequalities that provide deeper insights into the relationship between these two mathematical concepts. Beyond their theoretical significance, we also present practical implications of our results. Specifically, we show that the deduced results can be applied to get marginally stable discrete-time transfer functions in digital control systems. УДК 517.5 Деякі зауваження про аналітичні функції, пов'язані з многочленами Фібоначчі, та їхні застосування Досліджено зв'язок між деякими многочленами Фібоначчі та лемою Шварца в контексті комплексного аналізу та теорії керування. Хоча многочлени Фібоначчі традиційно пов'язують з комбінаторною математикою та рекурентними послідовностями, вони також відіграють важливу роль і в розкладах аналітичних функцій у степеневі ряди. Наведено варіант леми Шварца на основі першого многочлена Фібоначчі. Розглянуто граничну версію леми Шварца, на підставі якої одержано нові нерівності, що дали змогу глибше зрозуміти взаємозв'язок цих двох математичних понять. Окрім теоретичного значення наведено деякі практичні наслідки отриманих результатів. Показано, що одержані результати можна застосувати для побудови дискретних передатних функцій, стійких на межі, в цифрових системах керування. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9079 10.3842/umzh.v77i11.9079 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 11 (2025); 694–695 Український математичний журнал; Том 77 № 11 (2025); 694–695 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9079/10600 Copyright (c) 2025 Timur Düzenli, Bülent Nafi Örnek, Tuğba Akyel |
| spellingShingle | Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba Düzenli, Timur Örnek, Bülent Nafi Akyel, Tuğba Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title | Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title_alt | Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title_full | Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title_fullStr | Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title_full_unstemmed | Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title_short | Some remarks for analytic functions related to Fibonacci polynomials and their applications |
| title_sort | some remarks for analytic functions related to fibonacci polynomials and their applications |
| topic_facet | Fibonacci polynomials Schwarz lemma Principle of Subordination 30C80 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9079 |
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