Analytic Functions Related to a Balloon-Shaped Domain
One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/12/865 |
| _version_ | 1827574791968653312 |
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| author | Adeel Ahmad Jianhua Gong Isra Al-Shbeil Akhter Rasheed Asad Ali Saqib Hussain |
| author_facet | Adeel Ahmad Jianhua Gong Isra Al-Shbeil Akhter Rasheed Asad Ali Saqib Hussain |
| author_sort | Adeel Ahmad |
| collection | DOAJ |
| description | One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula> defined in the new domain, including the sharp estimates for the coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><msub><mi>a</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mn>4</mn></msub></semantics></math></inline-formula>, and for three second-order and third-order Hankel determinants, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">H</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mi mathvariant="script">X</mi><mo>,</mo><msub><mi mathvariant="script">H</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mi mathvariant="script">X</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">H</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mi mathvariant="script">X</mi></mrow></semantics></math></inline-formula>. The optimality of each obtained estimate is given as well. |
| first_indexed | 2024-03-08T20:46:05Z |
| format | Article |
| id | doaj.art-caaa627807a3412090fdae75cf532b1c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T20:46:05Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-caaa627807a3412090fdae75cf532b1c2023-12-22T14:10:00ZengMDPI AGFractal and Fractional2504-31102023-12-0171286510.3390/fractalfract7120865Analytic Functions Related to a Balloon-Shaped DomainAdeel Ahmad0Jianhua Gong1Isra Al-Shbeil2Akhter Rasheed3Asad Ali4Saqib Hussain5Department of Mathematics and Statistics, Hazara University Mansehra, Mansehra 21120, PakistanDepartment of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab EmiratesDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanDepartment of Mathematics, COMSATS University Islamabad, Abbottabad 22060, PakistanDepartment of Mathematics and Statistics, Hazara University Mansehra, Mansehra 21120, PakistanDepartment of Mathematics, COMSATS University Islamabad, Abbottabad 22060, PakistanOne of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula> defined in the new domain, including the sharp estimates for the coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><msub><mi>a</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mn>4</mn></msub></semantics></math></inline-formula>, and for three second-order and third-order Hankel determinants, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">H</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mi mathvariant="script">X</mi><mo>,</mo><msub><mi mathvariant="script">H</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mi mathvariant="script">X</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">H</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mi mathvariant="script">X</mi></mrow></semantics></math></inline-formula>. The optimality of each obtained estimate is given as well.https://www.mdpi.com/2504-3110/7/12/865analytic functionsubordinationsharp upper boundHankel determinantgeneralized domain |
| spellingShingle | Adeel Ahmad Jianhua Gong Isra Al-Shbeil Akhter Rasheed Asad Ali Saqib Hussain Analytic Functions Related to a Balloon-Shaped Domain Fractal and Fractional analytic function subordination sharp upper bound Hankel determinant generalized domain |
| title | Analytic Functions Related to a Balloon-Shaped Domain |
| title_full | Analytic Functions Related to a Balloon-Shaped Domain |
| title_fullStr | Analytic Functions Related to a Balloon-Shaped Domain |
| title_full_unstemmed | Analytic Functions Related to a Balloon-Shaped Domain |
| title_short | Analytic Functions Related to a Balloon-Shaped Domain |
| title_sort | analytic functions related to a balloon shaped domain |
| topic | analytic function subordination sharp upper bound Hankel determinant generalized domain |
| url | https://www.mdpi.com/2504-3110/7/12/865 |
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