Abstract:  In this paper, we establish a Rosenthal-type inequality of partial sums for ρ^--mixing random variables. As its applications, we get the complete convergence rates in the strong laws for ρ^--mixing random variables. The result obtained extends the corresponding result.

Key words: convergence rates, rosenthal type inequality, ρ^--mixing random variables, ρ-mixing random variables, negatively associated random variables