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In this paper we consider the asymptotic formula for the number of the solutions of the equation $p_1+p_2+p_3=N$ where $N$ is an odd integer and the unknowns $p_i$ are prime numbers of the form $p_i=\left[n^{1/{\gamma }_i}\right]$. We use the two-dimensional van der Corput’s method to prove it under less restrictive conditions than before. In the most interesting case ${\gamma }_1={\gamma }_2={\gamma }_3=\gamma$ our theorem implies that every sufficiently large odd integer $N$ may be written as the sum of three Piatetski-Shapiro primes of type $\gamma$ for $50/53$ < $\gamma$ < $1$.