A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition
In this paper, we introduce a special family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="fraktur">M</mi><msub><mi>σ</mi><mi>m&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/5/271 |
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| author | Ibtisam Aldawish Sondekola Rudra Swamy Basem Aref Frasin |
| author_facet | Ibtisam Aldawish Sondekola Rudra Swamy Basem Aref Frasin |
| author_sort | Ibtisam Aldawish |
| collection | DOAJ |
| description | In this paper, we introduce a special family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="fraktur">M</mi><msub><mi>σ</mi><mi>m</mi></msub></msub><mrow><mo>(</mo><mi>τ</mi><mo>,</mo><mi>ν</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>φ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of the function family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>σ</mi><mi>m</mi></msub></semantics></math></inline-formula> of <i>m</i>-fold symmetric bi-univalent functions defined in the open unit disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">D</mi></semantics></math></inline-formula> and obtain estimates of the first two Taylor–Maclaurin coefficients for functions in the special family. Further, the Fekete–Szegö functional for functions in this special family is also estimated. The results presented in this paper not only generalize and improve some recent works, but also give new results as special cases. |
| first_indexed | 2024-03-10T03:52:39Z |
| format | Article |
| id | doaj.art-dc7f9a1dcf6a4784ba82d0b51b55ab9c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T03:52:39Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-dc7f9a1dcf6a4784ba82d0b51b55ab9c2023-11-23T11:03:49ZengMDPI AGFractal and Fractional2504-31102022-05-016527110.3390/fractalfract6050271A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination ConditionIbtisam Aldawish0Sondekola Rudra Swamy1Basem Aref Frasin2Department of Mathematics and Statistics, College of Science, Imam Mohammad IBN Saud Islamic University, P.O. Box 90950, Riyadh 11623, Saudi ArabiaDepartment of Computer Science and Engineering, RV College of Engineering, Bengaluru 560 059, Karnataka, IndiaFaculty of Science, Department of Mathematics, Al Al-Bayt University, Mafraq 25113, JordanIn this paper, we introduce a special family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="fraktur">M</mi><msub><mi>σ</mi><mi>m</mi></msub></msub><mrow><mo>(</mo><mi>τ</mi><mo>,</mo><mi>ν</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>φ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of the function family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>σ</mi><mi>m</mi></msub></semantics></math></inline-formula> of <i>m</i>-fold symmetric bi-univalent functions defined in the open unit disc <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">D</mi></semantics></math></inline-formula> and obtain estimates of the first two Taylor–Maclaurin coefficients for functions in the special family. Further, the Fekete–Szegö functional for functions in this special family is also estimated. The results presented in this paper not only generalize and improve some recent works, but also give new results as special cases.https://www.mdpi.com/2504-3110/6/5/271bi-univalent functionscoefficient estimatesFekete–Szegö functional<i>m</i>-fold symmetric bi-univalent functions |
| spellingShingle | Ibtisam Aldawish Sondekola Rudra Swamy Basem Aref Frasin A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition Fractal and Fractional bi-univalent functions coefficient estimates Fekete–Szegö functional <i>m</i>-fold symmetric bi-univalent functions |
| title | A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition |
| title_full | A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition |
| title_fullStr | A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition |
| title_full_unstemmed | A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition |
| title_short | A Special Family of <i>m</i>-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition |
| title_sort | special family of i m i fold symmetric bi univalent functions satisfying subordination condition |
| topic | bi-univalent functions coefficient estimates Fekete–Szegö functional <i>m</i>-fold symmetric bi-univalent functions |
| url | https://www.mdpi.com/2504-3110/6/5/271 |
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