On Geometric Properties of a Certain Analytic Function with Negative Coefficients
Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/172 |
| _version_ | 1827648989836607488 |
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| author | Matthew Olanrewaju Oluwayemi Esther O. Davids Adriana Cătaş |
| author_facet | Matthew Olanrewaju Oluwayemi Esther O. Davids Adriana Cătaş |
| author_sort | Matthew Olanrewaju Oluwayemi |
| collection | DOAJ |
| description | Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>z</mi><mo>−</mo><msubsup><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>2</mn></mrow><mi>t</mi></msubsup><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mrow><mo>[</mo><mi>ω</mi><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mo>+</mo><mi>c</mi><mi>γ</mi><mo>−</mo><mi>σ</mi><mo>]</mo></mrow><msub><mi>C</mi><mi>m</mi></msub></mrow><mrow><mrow><mo>[</mo><mi>m</mi><mi>σ</mi><mo>−</mo><mi>c</mi><mi>ω</mi><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mo>+</mo><mi>c</mi><mi>γ</mi><mo>]</mo></mrow><msup><mi>K</mi><mi>n</mi></msup></mrow></mfrac></mstyle><msup><mi>z</mi><mi>m</mi></msup><mo>−</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>t</mi><mo>+</mo><mn>1</mn></mrow><mo>∞</mo></msubsup><msub><mi>a</mi><mi>k</mi></msub><msup><mi>z</mi><mi>k</mi></msup></mrow></semantics></math></inline-formula> is defined using a generalized differential operator. Furthermore, some geometric properties for the class were established. |
| first_indexed | 2024-03-09T19:49:41Z |
| format | Article |
| id | doaj.art-e0d5aadc5243441a808d28968d58033c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:41Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e0d5aadc5243441a808d28968d58033c2023-11-24T01:14:52ZengMDPI AGFractal and Fractional2504-31102022-03-016317210.3390/fractalfract6030172On Geometric Properties of a Certain Analytic Function with Negative CoefficientsMatthew Olanrewaju Oluwayemi0Esther O. Davids1Adriana Cătaş2Health and Well Being Research Group, Landmark University, SDG 3, Omu-Aran 251103, NigeriaHealth and Well Being Research Group, Landmark University, SDG 3, Omu-Aran 251103, NigeriaDepartment of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, RomaniaVarious function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>z</mi><mo>−</mo><msubsup><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>2</mn></mrow><mi>t</mi></msubsup><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mrow><mo>[</mo><mi>ω</mi><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mo>+</mo><mi>c</mi><mi>γ</mi><mo>−</mo><mi>σ</mi><mo>]</mo></mrow><msub><mi>C</mi><mi>m</mi></msub></mrow><mrow><mrow><mo>[</mo><mi>m</mi><mi>σ</mi><mo>−</mo><mi>c</mi><mi>ω</mi><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mo>+</mo><mi>c</mi><mi>γ</mi><mo>]</mo></mrow><msup><mi>K</mi><mi>n</mi></msup></mrow></mfrac></mstyle><msup><mi>z</mi><mi>m</mi></msup><mo>−</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>t</mi><mo>+</mo><mn>1</mn></mrow><mo>∞</mo></msubsup><msub><mi>a</mi><mi>k</mi></msub><msup><mi>z</mi><mi>k</mi></msup></mrow></semantics></math></inline-formula> is defined using a generalized differential operator. Furthermore, some geometric properties for the class were established.https://www.mdpi.com/2504-3110/6/3/172analytic functionsunivalent functioncoefficient estimatesfixed coefficientsextreme points |
| spellingShingle | Matthew Olanrewaju Oluwayemi Esther O. Davids Adriana Cătaş On Geometric Properties of a Certain Analytic Function with Negative Coefficients Fractal and Fractional analytic functions univalent function coefficient estimates fixed coefficients extreme points |
| title | On Geometric Properties of a Certain Analytic Function with Negative Coefficients |
| title_full | On Geometric Properties of a Certain Analytic Function with Negative Coefficients |
| title_fullStr | On Geometric Properties of a Certain Analytic Function with Negative Coefficients |
| title_full_unstemmed | On Geometric Properties of a Certain Analytic Function with Negative Coefficients |
| title_short | On Geometric Properties of a Certain Analytic Function with Negative Coefficients |
| title_sort | on geometric properties of a certain analytic function with negative coefficients |
| topic | analytic functions univalent function coefficient estimates fixed coefficients extreme points |
| url | https://www.mdpi.com/2504-3110/6/3/172 |
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