Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions
In the current work, we introduce a special family of the function family of analytic and m-fold symmetric bi-univalent functions and obtain estimates of the Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"&g...
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1165 |
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| author | Sondekola Rudra Swamy Basem Aref Frasin Ibtisam Aldawish |
| author_facet | Sondekola Rudra Swamy Basem Aref Frasin Ibtisam Aldawish |
| author_sort | Sondekola Rudra Swamy |
| collection | DOAJ |
| description | In the current work, we introduce a special family of the function family of analytic and m-fold symmetric bi-univalent functions and obtain estimates of the Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for functions in the special family. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> a real number, Fekete–Szegö functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>−</mo><mi>δ</mi><msubsup><mi>d</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></msubsup><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for functions in the special family is also estimated. We indicate several cases of the defined family and connections to existing results are also discussed. |
| first_indexed | 2024-03-09T11:38:23Z |
| format | Article |
| id | doaj.art-982ca55390874d77a43d47dc6a5d9d00 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:23Z |
| publishDate | 2022-04-01 |
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| series | Mathematics |
| spelling | doaj.art-982ca55390874d77a43d47dc6a5d9d002023-11-30T23:38:06ZengMDPI AGMathematics2227-73902022-04-01107116510.3390/math10071165Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent FunctionsSondekola Rudra Swamy0Basem Aref Frasin1Ibtisam Aldawish2Department of Computer Science and Engineering, RV College of Engineering, Bengaluru 560 059, IndiaDepartment of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, JordanDepartment of Mathematics and Statistics, College of Science, Imam Mohammad IBN Saud Islamic University, Riyadh 11623, Saudi ArabiaIn the current work, we introduce a special family of the function family of analytic and m-fold symmetric bi-univalent functions and obtain estimates of the Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for functions in the special family. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> a real number, Fekete–Szegö functional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msub><mi>d</mi><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>−</mo><mi>δ</mi><msubsup><mi>d</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></msubsup><mrow><mo>|</mo></mrow></mrow></semantics></math></inline-formula> for functions in the special family is also estimated. We indicate several cases of the defined family and connections to existing results are also discussed.https://www.mdpi.com/2227-7390/10/7/1165bi-univalent functionscoefficient estimatesFekete–Szegö functionalm-fold symmetric bi-univalent functions |
| spellingShingle | Sondekola Rudra Swamy Basem Aref Frasin Ibtisam Aldawish Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Mathematics bi-univalent functions coefficient estimates Fekete–Szegö functional m-fold symmetric bi-univalent functions |
| title | Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_full | Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_fullStr | Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_full_unstemmed | Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_short | Fekete–Szegö Functional Problem for a Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_sort | fekete szego functional problem for a special family of i m i fold symmetric bi univalent functions |
| topic | bi-univalent functions coefficient estimates Fekete–Szegö functional m-fold symmetric bi-univalent functions |
| url | https://www.mdpi.com/2227-7390/10/7/1165 |
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