Titlebook: On Global Univalence Theorems; T. Parthasarathy Book 1983 Springer-Verlag Berlin Heidelberg 1983 Differenzierbare Abbildung.Finite.Funktio

消耗

新娘

cathartic

易怒

Fundamental global univalence results of Gale-Nikaido-Inada,o the problem under consideration. One approach places topological assumptions on the map and the other places further conditions on the Jacobian matrices. We will study the former in the next chapter and the latter in the present chapter.

HEED

Global univalent results in R2 and R3, assumption that the diagonal entries are identically zero will imply that F is one-one in any open convex region in R.-this result supplements the result obtained by Gale and Nikaido. We can weaken our assumptions in rectangular regions in R. using Garcia-Zangwill‘s result given in the previous chapter.

帶傷害

defendant

Assorted applications of univalence mapping results,distribution is infinitely divisible. In this situation weak N-matrices play an important role. There are various other applications (for example to nonlinear net-work theory) but we will not attempt to exhaust all of them for lack of time and space. [We have already seen a nice application of univalent results in stability theory in chapter VII].

ALLEY

Global homeomorphisms between finite dimensional spaces,to More and Rheinboldt and this result will then be used to prove Gale-Nikaido‘s theorem under weaker assumptions. In the last section we will prove a result due to McAuley for light open mappings. We will end this chapter with an old conjecture of Whyburn.