A fixed point theorem for contraction-mapping on p-distance space

According to the basic concepts of metric space and 2-metric space,in this paper,the concepts of p-metric space and the basic concepts on p-distance space are introduced.Conformed to the ideas and methodsfor studying fixed point theory on 2-metric space,and make use of the theory in functional analysis.I studied the fixed point problem on p-distance space. And transplanted fixed point theory on 2-distance space to p-distance space.So that formed some basic theory of fixed point on p-distance space.In the end,the metric space,2-metric space and 3-metric space are the special of p-metric space.