Coefficient Inequalities For Two New Subclasses of Bi-univalent Functions Involving Lucas-Balancing Polynomials

In this article, by making use of Lucas-Balancing polynomials two new subclasses of bi-univalent functions are introduced. Then we establish the bounds for the initial Taylor–Maclaurin coefficients |a_2 | and |a_3 | for a new family of analytic and bi-univalent functions in the open unit disk which involve Lucas-Balancing polynomials. Furthermore, we investigate the special cases and consequences for the new family functions. In addition, the Fekete-Szegö problem is handled for the functions belonging to these new subclasses.