The Application Of Nonlinear Method In Interval Analysis

In this paper, the metric spaces of interval numbers is constructed under a distance between two interval numbers, and its completeness is proved. Then, we define the par-tial order on it, getting several fixed point theorems in partially ordered metric space of interval numbers. Then, we apply the Hausdorff distance of two sets on the n-dimensional interval vectors, and a simpler distance formula is given. In this article, we also define the infinite dimensional interval vectors and its arithmetic on the basis of n-dimensional interval vectors, and some properties of these operations are discussed. Then, following the distance of interval numbers, a specific distance formula between the two infinite di-mensional interval vectors is got by defining the vector model. Then,we show the more general representation of metric and a specific calculation example on interval vector space of infinite dimension. Secondly, the completeness problem for measurement on the metric space of infinite dimensional interval vectors is discussed, and we get the inner link of the completeness between the metric space of infinite dimensional interval vectors and the metric space of interval numbers. Finally, a fixed point theorem on the metric space of infinite dimensional interval vector is given on this basis.