Abstract: In this paper we introduce a new general subclass n,G∑ a,λ（A, B, α） of univalent functions related the known integral operator and differential operator. Some majorization results for n,G∑ a,λ（A, B, 1） as well as the other functions are given. Furthermore, we find the coefficients bounds on |a2| and |a3| for functions in*n,G∑ a,λ（A₁, B₁, A₂, B₂, α₁, α₂）, which is the bi-univalent functions defined by n,G ∑a,λ（A, B, α） and subordination. By giving specific values of the parameters of our main results, several（known or new） consequences of main results are also discussed. 

Key words: analytic functions, integral operator, majorization, subordination, bi-univalent functions