Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials

Abstract

In this paper, we introduced two novel subclasses of bi-univalent functions, $ \mathcal{M}_{\Sigma}(\alpha, \mathcal{B}(x, \xi)) $ and $ \mathcal{H}_{\Sigma}(\alpha, \mu, \mathcal{B}(x, \xi)) $, utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients $ \left|a_2\right| $ and $ \left|a_3\right| $, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization.

Keywords

• balancing polynomial
• lucas-balancing polynomials
• bi-univalent functions
• analytic functions
• taylor-maclaurin coefficients
• fekete-szegö functional