Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials
By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/7/360 |
| _version_ | 1797433625987252224 |
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| author | Sheza M. El-Deeb Alina Alb Lupaş |
| author_facet | Sheza M. El-Deeb Alina Alb Lupaş |
| author_sort | Sheza M. El-Deeb |
| collection | DOAJ |
| description | By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics></math></inline-formula>, in the open unit disc with respect to symmetric conjugate points connected with the combination Binomial series and Babalola operator. The bounds on the initial coefficients <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfenced close="|" open="|"><msub><mi>a</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula> and <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfenced close="|" open="|"><msub><mi>a</mi><mn>3</mn></msub></mfenced></semantics></math></inline-formula> for the functions in this new subclass of <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics></math></inline-formula> are investigated. Moreover, we obtain an estimation for the Fekete–Szego problem for the function subclass defined in this paper. Relevant connections of these results are presented here as corollaries. |
| first_indexed | 2024-03-09T10:18:45Z |
| format | Article |
| id | doaj.art-d34ef7f80b844adba8c08d949381c4a6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T10:18:45Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d34ef7f80b844adba8c08d949381c4a62023-12-01T22:10:27ZengMDPI AGFractal and Fractional2504-31102022-06-016736010.3390/fractalfract6070360Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas PolynomialsSheza M. El-Deeb0Alina Alb Lupaş1Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, EgyptDepartment of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, RomaniaBy using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics></math></inline-formula>, in the open unit disc with respect to symmetric conjugate points connected with the combination Binomial series and Babalola operator. The bounds on the initial coefficients <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfenced close="|" open="|"><msub><mi>a</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula> and <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfenced close="|" open="|"><msub><mi>a</mi><mn>3</mn></msub></mfenced></semantics></math></inline-formula> for the functions in this new subclass of <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics></math></inline-formula> are investigated. Moreover, we obtain an estimation for the Fekete–Szego problem for the function subclass defined in this paper. Relevant connections of these results are presented here as corollaries.https://www.mdpi.com/2504-3110/6/7/360symmetric conjugate pointsbi-univalent functionsLucas polynomialsbinomial seriesBabalola operator |
| spellingShingle | Sheza M. El-Deeb Alina Alb Lupaş Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials Fractal and Fractional symmetric conjugate points bi-univalent functions Lucas polynomials binomial series Babalola operator |
| title | Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials |
| title_full | Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials |
| title_fullStr | Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials |
| title_full_unstemmed | Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials |
| title_short | Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials |
| title_sort | coefficient estimates for the functions with respect to symmetric conjugate points connected with the combination binomial series and babalola operator and lucas polynomials |
| topic | symmetric conjugate points bi-univalent functions Lucas polynomials binomial series Babalola operator |
| url | https://www.mdpi.com/2504-3110/6/7/360 |
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