Bi-univalent functions connected to Bazilevič and $ \lambda $-Pseudo functions and their Lucas-Balancing polynomial applications

In this work, we define two families $ \mathcal{V}_{\Sigma }(\mu, \gamma, \lambda; r) $ and $ \mathcal{W}_{\Sigma }(\mu, \gamma, \lambda; r) $ of holomorphic and bi-univalent functions connected with Bazilevič functions and $ \lambda $-pseudo functions defined by Lucas-Balancing polynomials. We demonstrate the upper bounds for the initial Taylor-Maclaurin coefficients. In addition, the Fekete-Szegö type inequalities are derived for functions in these families. Moreover, we indicate certain special cases and consequences for our results.