Applications of Shell-like Curves Connected with Fibonacci Numbers
We introduce a new subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold">J</mi><msup><mrow><mo>Σ</mo></mrow><mrow><mi&...
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| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/7/639 |
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| author | Ala Amourah Ibtisam Aldawish Basem Aref Frasin Tariq Al-Hawary |
| author_facet | Ala Amourah Ibtisam Aldawish Basem Aref Frasin Tariq Al-Hawary |
| author_sort | Ala Amourah |
| collection | DOAJ |
| description | We introduce a new subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold">J</mi><msup><mrow><mo>Σ</mo></mrow><mrow><mi>η</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>μ</mi></mrow></msup><mrow><mo>(</mo><mover accent="true"><mi>p</mi><mo>˜</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of bi-univalent functions, defined by shell-like curves connected with Fibonacci numbers. Our main results in this paper include estimates of the Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="|" close="|"><msub><mi>a</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="|" close="|"><msub><mi>a</mi><mn>3</mn></msub></mfenced></semantics></math></inline-formula> for functions in this subclass, as well as solutions to Fekete–Szegö functional problems. We also show novel outcomes resulting from the specialization of the parameters used in our main results. |
| first_indexed | 2024-03-11T01:18:55Z |
| format | Article |
| id | doaj.art-c5be427d3e2148aea2ad03bbdfa611cc |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T01:18:55Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-c5be427d3e2148aea2ad03bbdfa611cc2023-11-18T18:17:22ZengMDPI AGAxioms2075-16802023-06-0112763910.3390/axioms12070639Applications of Shell-like Curves Connected with Fibonacci NumbersAla Amourah0Ibtisam Aldawish1Basem Aref Frasin2Tariq Al-Hawary3Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, JordanDepartment of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh 11566, Saudi ArabiaFaculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, JordanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanWe introduce a new subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold">J</mi><msup><mrow><mo>Σ</mo></mrow><mrow><mi>η</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>μ</mi></mrow></msup><mrow><mo>(</mo><mover accent="true"><mi>p</mi><mo>˜</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of bi-univalent functions, defined by shell-like curves connected with Fibonacci numbers. Our main results in this paper include estimates of the Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="|" close="|"><msub><mi>a</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="|" close="|"><msub><mi>a</mi><mn>3</mn></msub></mfenced></semantics></math></inline-formula> for functions in this subclass, as well as solutions to Fekete–Szegö functional problems. We also show novel outcomes resulting from the specialization of the parameters used in our main results.https://www.mdpi.com/2075-1680/12/7/639Fekete–Szegö problembi-univalent functionsFibonacci numbersanalytic functionsshell-like curve |
| spellingShingle | Ala Amourah Ibtisam Aldawish Basem Aref Frasin Tariq Al-Hawary Applications of Shell-like Curves Connected with Fibonacci Numbers Axioms Fekete–Szegö problem bi-univalent functions Fibonacci numbers analytic functions shell-like curve |
| title | Applications of Shell-like Curves Connected with Fibonacci Numbers |
| title_full | Applications of Shell-like Curves Connected with Fibonacci Numbers |
| title_fullStr | Applications of Shell-like Curves Connected with Fibonacci Numbers |
| title_full_unstemmed | Applications of Shell-like Curves Connected with Fibonacci Numbers |
| title_short | Applications of Shell-like Curves Connected with Fibonacci Numbers |
| title_sort | applications of shell like curves connected with fibonacci numbers |
| topic | Fekete–Szegö problem bi-univalent functions Fibonacci numbers analytic functions shell-like curve |
| url | https://www.mdpi.com/2075-1680/12/7/639 |
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