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Faber Polynomial Coefficient Estimates of m -Fold Symmetric Bi-Univalent Functions with Bounded Boundary Rotation

Author

Listed:
  • Anandan Murugan

    (Department of Mathematics, College of Engineering Guindy, Anna University, Chennai 600025, Tamilnadu, India)

  • Srikandan Sivasubramanian

    (Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India)

  • Prathviraj Sharma

    (Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India)

  • Gangadharan Murugusundaramoorthy

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamilnadu, India)

Abstract

In the current article, we introduce several new subclasses of m -fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk D . Utilizing the Faber polynomial expansion, we derive upper bounds for the coefficients | b m k + 1 | and establish initial coefficient bounds for | b m + 1 | and | b 2 m + 1 | . Additionally, we explore the Fekete–Szegö inequalities applicable to the functions that fall within these newly defined subclasses.

Suggested Citation

  • Anandan Murugan & Srikandan Sivasubramanian & Prathviraj Sharma & Gangadharan Murugusundaramoorthy, 2024. "Faber Polynomial Coefficient Estimates of m -Fold Symmetric Bi-Univalent Functions with Bounded Boundary Rotation," Mathematics, MDPI, vol. 12(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3963-:d:1545571
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