Assorted applications of univalence mapping results

Abstract

In this chapter we will give various applications of the univalence results proved in the earlier chapters. There are several areas where univalence results are quite handy and useful. The first application will deal with a problem in Mathematical Economics where we will give a set of sufficient conditions due to Nikaido and Mas-Colell which will ensure factor price equalization. The second application deals with the distribution of a function of several independent random variables. As a third application we will consider a problem in nonlinear complimentarity theory due to Kojima and Megiddo. Next we give an application of Hadamard's theorem to Algebra. In the fifth we consider the problem of deciding whether a certain multivariate gamma 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].