In this paper, the concept of p-metric space is introduced.According to the theory of functional analysis, the fixed point problems on p-metric space are studied. A common fixed-point theorem for a series of contraction mappings on p-metric space is also given, in which the metric space 2-metric space and 3-metric space are the special cases of p-metric space.%引入了p-距离空间的概念，利用海鲜函分析的理论，对p-距离空间中的不动点问题进行了研究，给出了p-距离空间中一类压缩映像序列的公共不动点定理。其距离空间、2-距离空间和3-距离空间都是p-距离空间的特殊例子。
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