In this paper, we generalize some matrix inequalities involving the matrix power means and Karcher mean of positive definite matrices. Among other inequalities, it is shown that if A = (A 1 , · · · , A n) is an n-tuple of positive definite matrices such that 0 < m ≤ A i ≤ M (i = 1, · · · , n) for some scalars m < M and ω = (w 1 , · · · , w n) is a weight vector with w i ≥ 0 and ∑n i=1 w i = 1, then Φ p (∑n i=1 w i A i) ≤ α p Φ p (P t (ω; A)) and Φ p (∑n i=1 w i A i) ≤ α p Φ p (Λ(ω; A)), where p > 0, α = max {(M+m) 2 4Mm , (M+m) 2 4 2 p Mm}, Φ is a positive unital linear map and t ∈ [−1, 1]\{0}.