For any homogeneous polynomial, it can be expressed as the product of a tensor A and a vector x, we denote it by P A (x). With the change of the norm of x, the maximum value (resp. the minimum value) of P A (x) is changed. In this paper, by the properties of tensor A, we study the relationships between the maximum values (resp. minimum values) of P A (x) under different norms of x. We present that the maximum values (resp. the minimum values) of P A (x) at different norms of x always have the same sign. Moreover, the relationship between the magnitudes of the maximum values (resp. the minimum values) of P A (x) at different norms of x are characterized. Further, some inequalities on H-eigenvalues and Z-eigenvalues of tensor A are obtained directly. And some applications on definite positive of tensors and hypergraphs are given.