Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions
In the current article, making use of certain operator, we initiate and explore a certain family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">W</m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/4/595 |
| _version_ | 1797478317932150784 |
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| author | Abbas Kareem Wanas Luminiţa-Ioana Cotîrlă |
| author_facet | Abbas Kareem Wanas Luminiţa-Ioana Cotîrlă |
| author_sort | Abbas Kareem Wanas |
| collection | DOAJ |
| description | In the current article, making use of certain operator, we initiate and explore a certain family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">W</mi><mo>Σ</mo></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>h</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of holomorphic and bi-univalent functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">D</mi></semantics></math></inline-formula>. We establish upper bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö type inequality for functions in this family. |
| first_indexed | 2024-03-09T21:30:16Z |
| format | Article |
| id | doaj.art-313c1dfd18894b0aa30b7a1a45b9eec3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:16Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-313c1dfd18894b0aa30b7a1a45b9eec32023-11-23T20:57:12ZengMDPI AGMathematics2227-73902022-02-0110459510.3390/math10040595Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent FunctionsAbbas Kareem Wanas0Luminiţa-Ioana Cotîrlă1Department of Mathematics, College of Science, University of Al-Qadisiyah, Al-Qadisiyah 58001, IraqDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaIn the current article, making use of certain operator, we initiate and explore a certain family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">W</mi><mo>Σ</mo></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>h</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of holomorphic and bi-univalent functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">D</mi></semantics></math></inline-formula>. We establish upper bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö type inequality for functions in this family.https://www.mdpi.com/2227-7390/10/4/595(<i>M</i>,<i>N</i>)-Lucas polynomialsbi-univalent functionupper boundsholomorphic functionFekete–Szegö problem |
| spellingShingle | Abbas Kareem Wanas Luminiţa-Ioana Cotîrlă Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions Mathematics (<i>M</i>,<i>N</i>)-Lucas polynomials bi-univalent function upper bounds holomorphic function Fekete–Szegö problem |
| title | Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions |
| title_full | Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions |
| title_fullStr | Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions |
| title_full_unstemmed | Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions |
| title_short | Applications of (<i>M</i>,<i>N</i>)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions |
| title_sort | applications of i m i i n i lucas polynomials on a certain family of bi univalent functions |
| topic | (<i>M</i>,<i>N</i>)-Lucas polynomials bi-univalent function upper bounds holomorphic function Fekete–Szegö problem |
| url | https://www.mdpi.com/2227-7390/10/4/595 |
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