Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions

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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Bibliographic Details
Main Authors:	Gangadharan Murugusundaramoorthy, Luminita-Ioana Cotîrlă, Daniel Breaz, Sheza M. El-Deeb
Format:	Article
Language:	English
Published:	MDPI AG 2025-01-01
Series:	Axioms
Subjects:	analytic functions univalent and bi-univalent functions convolution Taylor–Maclaurin series starlike functions convex functions
Online Access:	https://www.mdpi.com/2075-1680/14/1/50
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Summary:	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.
ISSN:	2075-1680