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Abstract Let A 1 , A 2 , … , A k $A_{1}, A_{2},\ldots, A_{k}$ be nonnegative matrices. In this paper, some upper bounds for the spectral radius ρ ( A 1 ∘ A 2 ∘ ⋯ ∘ A k ) $\rho(A_{1}\circ A_{2}\circ\cdots\circ A_{k})$ are proposed. These bounds generalize some existing results, and comparisons between these bounds are also considered.