Total Positivity of A Kind of Generalized Toric-Bernstein Basis

The normalized totally positive basis is a set of basis functions defined on the parameter domain $\Xi$, which satisfies the properties of non-negative and partition of the unit, meanwhile the collocation matrix of basis on arbitrary increasing real sequence is a totally positive matrix. Based on the generalized Vandermonde determinant defined on real points, the normalized total positivity of a kind of generalized toric-Bernstein basis is proved, which are defined on a set of real points.