A generalization of two refined Young inequalities

We prove that if a, b > 0 and 0 <= nu <= 1, then for m = 1, 2, 3,..., we have (a(nu)b(1-nu))(m) + r(0)(m) (a(m/2) - b(m/2))(2) <= (nu a + (1 - nu)b)(m), where r(0) = min {nu, 1 - nu}. This is a considerable generalization of two refinements of the classical Young inequality due to Kittaneh and Manasrah, and Hirzallah and Kittaneh, which correspond to the cases m = 1 and m = 2, respectively. As applications of this inequality, we give refined Young- type inequalities for the traces, determinants, and norms of positive definite matrices.