By using the conditions of compatible and subcompatible mapping pair in 2-metric spaces,the existence and the uniqueness of common fixed point for a class of Φ-contractive mappings in complete 2-metric spaces is discussed.

By the condition of compatible mapping pair and subcompatible mapping pair in 2-metric spaces,the paper discusses the existence and the uniqueness of common fixed point for a class of twice power type Φ-contractive mapping in complete 2-metric spaces.

In this paper,by introducing the concept of a couple of asymptotically reqular mappings,a exist- ence theorem of common fixed point is derived under suitable assumptions in complete metric spaces.

It is obtained that if (Z,d) is a eomplete 2-mettic space then (CB (Z), H) is also a complete 2-metric space.

Let (X,d ) be a complete 2-metric space, A,B are two mappings of expansion from X to X.

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.

This Paper Introduces a New Generalized Contractive Mapping in 2-distance Spaces and Discusses the Existance and Uniqueness of Its Fixed Piont.