Gegenbauer Polynomials for a Subfamily of Bi-univalent Functions

We study a subfamily of bi-univalent and regular functions in the open unit disk subordinate to Gegenbauer polynomials. For functions in the defined subfamily, we derive initial coefficients bounds. Additionally, the Fekete-Szegö problem is handled for the elements of the defined subfamily. We also discuss relevant connections to previous findings and several fresh outcomes are shown to follow.