Generalized bivariate Fibonacci polynomials for a comprehensive subfamily of bi-univalent functions

Swamy, Sondekola Rudra

doi:10.22075/ijnaa.2025.37562.5452

Generalized bivariate Fibonacci polynomials for a comprehensive subfamily of bi-univalent functions

Articles in Press

Document Type : Research Paper

Author

Sondekola Rudra Swamy

Department of Information Science and Engineering, Acharya Institute of Technology, Bengaluru- 560 107, Karnataka, India

10.22075/ijnaa.2025.37562.5452

Abstract

Our present investigation is primarily motivated by the broad and impactful applications of special polynomials in geometric function theory. In particular, the generalized bivariate Fibonacci polynomials have recently attracted attention in the study of bi-univalent functions. In this article, we introduce and analyze a comprehensive subfamily of bi-univalent functions characterized by these generalized Fibonacci polynomials in two variables. This polynomial sequence is chosen due to its flexibility, as numerous other polynomial families can be derived through appropriate specialization of its parameters. By applying the subordination technique, we derive bounds for the initial coefficients of functions belonging to this subfamily and investigate the associated Fekete–Szegö problem. In addition to presenting several new findings, we also explore meaningful connections with previously established results in the theory of bi-univalent and subordinate functions, thereby extending and unifying existing literature in a novel direction.

Keywords

Holomorphic functions

generalized bivariate Fibonacci polynomials

bi-univalent functions

subordination

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