Turan inequalities for the broken k-diamond partition functions

We obtain an asymptotic formula for Andrews and Paule's broken k-diamond partition function triangle(k)(n) where k=1 or 2. Based on this asymptotic formula, we derive that triangle(k)(n) satisfies the order d Turan inequalities for d >= 1 and for sufficiently large n when k=1 and 2 by using a general result of Griffin, Ono, Rolen and Zagier. We also show that Andrews and Paule's broken k-diamond partition function triangle(k)(n) is log-concave for n >= 1 when k=1 and 2. This leads to triangle(k) (a) triangle(k) (b)>= triangle(k) (a+b) for a,b >= 1 when k=1 and 2.