The ternary Goldbach-Vinogradov theorem with almost equal primes from the Beatty sequence.

Let α, α, α, β, β, β be real numbers with α, α, α >1. Suppose that each individual α is of a finite type and that at least one pair $\alpha_{i}^{-1}$, $\alpha_{j}^{-1}$ is also of a finite type. In this paper we prove that every large odd integer n can be represented as with p= n/3+ O( n(log n)) and $p_{i}\in\mathcal{B}_{i}$, where c>0 is an absolute constant and $\mathcal{B}_{i}$ denotes the so-called Beatty sequence, i.e. [ABSTRACT FROM AUTHOR]