New subclasses of bi-univalent functions connected with a q- analogue of convolution based upon the Legendre polynomials

In this paper, we introduce new subclasses of analytic and bi-univalent functions connected with a q-analogue of convolution by using the Legender  polynomials. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses.