Estimations of the coefficients of Horadam polynomials for certain subclasses of bi-univalent Bazilevich functions

UDC 517.5 We propose to use the Horadam polynomials, which are known to include some potentially useful polynomials, such as the Pell polynomials, the Chebyshev polynomials of the second kind, the Fibonacci polynomials, the Pell–Lucas polynomials, and the Lucas polynomials. First, we use the Horadam polynomials to define a new class of bi-univalent functions. Then we establish estimates for the coefficients of inequalities $|c_{2}|$ and $|c_3|$ and consider the celebrated Fekete–Szegö problem for functions that belong to this new class of bi-univalent functions. We also provide relevant connections of our results with the results obtained in earlier investigations.