ON COEFFICIENT PROBLEM OF BI-UNIVALENT FUNCTIONS RELATED TO BERNOULLI POLYNOMIALS

Many researchers recently investigated several interesting subclasses of the class of bi-univalent functions and found non-sharp estimates on the first two Taylor-Maclaurin coefficients using some special polynomials like Faber, Lucas, Chebyshev, Horadam, Bernoulli, Gegenbauer, Pell-Lucas, Fibonacci, and their generalizations. The main objective of the paper is to introduce a new subclass of bi-univalent functions associated with the Bernoulli polynomials and q-derivative operator. We investigate the estimates for the Taylor-Maclaurin coefficients |a2|, |a3| and bounds for Fekete-Szeg? inequality. The results in this paper would generalize and improve the related works of several earlier authors.