Proof of an inequality related to the Omega-matrix

摘要

This paper gives a complement to the proof of our previous papers, which discussed about some properties of the solution curves of a nonlinear equation obtained from F(x) + Ax = b by deleting the first equation. The theorem is obtained under the assumption that A is an Ω-matrix. By showing rigorously the proof of the previous papers, we confirm that the solution curves possess neither maximal point nor inflection point with respect to the variable x_1.