Search

In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality. As application, we prove the uniqueness of the solution of initial value problem involving higher order partial differential equation. Mathematics subject classification (2010): 26D15.

The well-known question for dual quermassintegrals is following: For which values of i ∈ N and every pair of star bodies K and L , is it true that Wi(K+L) Wi+1(K+L) Wi(K) Wi+1(K) + Wi(L) Wi+1(L) ? In 2005, the inequality was proved if i = n−1 or i = n−2 . But, now the question is not solved completely for 0 i n− 3 and every pair of star bodies K and L . In the paper, we will give a completely answer for the dual question. Mathematics subject classification (2010): 52A30, 52A40.

Some new inequalities for i -th mixed p -affine surface area are established. The results in special cases yield some of the recent results on inequalities of this type. Mathematics subject classification (2010): 52A20.