Representation of Bi-Univalent Functions to Lucas Balancing Polynomials with Geometric Properties and Coefficient Bounds

Authors

  • Stalin Thangamani Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R & D Institute of Science and Technology, Avadi, Chennai 600062, India
  • Pshtiwan Othman Mohammed Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
  • Jeno Francis Devadoss Department of Mathematics, Prathyusha Engineering College, Anna University, Chennai 602025, India
  • Majeed Ahmad Yousif Department of Mathematics, College of Education, University of Zakho, Duhok 42001, Iraq
  • Meraa Arab 5Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia
  • Dumitru Baleanu Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6294

Keywords:

Bi-univalent functions, Lucas polynomial, Fekete-Szeg{\"o} inequality

Abstract

In this paper, we introduce and analyze a new subclass of bi-univalent functions defined in the open unit disk, associated with Lucas and Lucas balancing polynomials. By employing the Taylor-Maclaurin series expansion, precise bounds for the second and third coefficients,  $|a_2|$ and $|a_3|$ , are obtained. These estimates lead to important geometric interpretations related to the distortion, growth, and structural behavior of the functions near the origin. Furthermore, the mapping characteristics of these functions are examined in connection with existing bi-univalent subclasses. Special emphasis is placed on deriving a Fekete-Szegö type inequality for the proposed class, thereby extending earlier contributions in the field. The findings presented here are valuable for applications in geometric function theory and areas like fluid mechanics, conformal mappings, and engineering models where the analytic structure of bi-univalent functions plays a significant role.

Author Biography

  • Pshtiwan Othman Mohammed, Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq

    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186
    Rome, Italy

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Functional Analysis

License

Copyright (c) 2025 Stalin Thangamani, Pshtiwan Othman Mohammed, Jeno Francis Devadoss, Majeed Ahmad Yousif, Meraa Arab, Dumitru Baleanu

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How to Cite

Representation of Bi-Univalent Functions to Lucas Balancing Polynomials with Geometric Properties and Coefficient Bounds. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6294. https://doi.org/10.29020/nybg.ejpam.v18i3.6294