Sign-Change Diminishing Systems of Functions of Many Variables Original Research Article

Given functions ƒ1(x), ..., ƒn(x), x = (x1, ..., xm) ∈ M, where M is an open parallelepiped or simplex, let all minors of the matrix [formula] be positive for all x ∈ M. It is shown that if the sequence y1 − x1, .., ym − xm with (x1, ..., xm), (y1, ..., ym) ∈ M has k sign-changes, then there are no more than k sign changes in the sequence ƒ1(y) −ƒ1(x), ..., ƒn(y) − ƒn(x).