Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions
The Lucas balancing polynomial is linked to a family of bi-starlike functions denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">S</mi>...
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2025-01-01
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| author | Gangadharan Murugusundaramoorthy Luminita-Ioana Cotîrlă Daniel Breaz Sheza M. El-Deeb |
| author_facet | Gangadharan Murugusundaramoorthy Luminita-Ioana Cotîrlă Daniel Breaz Sheza M. El-Deeb |
| author_sort | Gangadharan Murugusundaramoorthy |
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| description | The Lucas balancing polynomial is linked to a family of bi-starlike functions denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">S</mi><mrow><mi>s</mi><mi>c</mi></mrow><mi>c</mi></msubsup><mrow><mo>(</mo><mi>ϑ</mi><mo>,</mo><mo>Ξ</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, which we present and examine in this work. These functions are defined with respect to symmetric conjugate points. Coefficient estimates are obtained for functions in this family. The classical Fekete–Szegö inequality of functions in this family is also obtained. |
| format | Article |
| id | doaj-art-676d42bcccbc4fdcad434ce5cf52a4f9 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-676d42bcccbc4fdcad434ce5cf52a4f92025-01-24T13:22:16ZengMDPI AGAxioms2075-16802025-01-011415010.3390/axioms14010050Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike FunctionsGangadharan Murugusundaramoorthy0Luminita-Ioana Cotîrlă1Daniel Breaz2Sheza M. El-Deeb3School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, IndiaDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaDepartment of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, RomaniaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaThe Lucas balancing polynomial is linked to a family of bi-starlike functions denoted as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">S</mi><mrow><mi>s</mi><mi>c</mi></mrow><mi>c</mi></msubsup><mrow><mo>(</mo><mi>ϑ</mi><mo>,</mo><mo>Ξ</mo><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, which we present and examine in this work. These functions are defined with respect to symmetric conjugate points. Coefficient estimates are obtained for functions in this family. The classical Fekete–Szegö inequality of functions in this family is also obtained.https://www.mdpi.com/2075-1680/14/1/50analytic functionsunivalent and bi-univalent functionsconvolutionTaylor–Maclaurin seriesstarlike functionsconvex functions |
| spellingShingle | Gangadharan Murugusundaramoorthy Luminita-Ioana Cotîrlă Daniel Breaz Sheza M. El-Deeb Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions Axioms analytic functions univalent and bi-univalent functions convolution Taylor–Maclaurin series starlike functions convex functions |
| title | Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions |
| title_full | Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions |
| title_fullStr | Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions |
| title_full_unstemmed | Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions |
| title_short | Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions |
| title_sort | applications of lucas balancing polynomial to subclasses of bi starlike functions |
| topic | analytic functions univalent and bi-univalent functions convolution Taylor–Maclaurin series starlike functions convex functions |
| url | https://www.mdpi.com/2075-1680/14/1/50 |
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