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Metric space has very important role in mathematics and its application. Gahler (1963) introduced the concept of 2-metric as a possible generalization of usual notion of a metric space. In many cases the results obtained in the usual metric spaces and 2-metric spaces are found to be unrelated (Sharma, 1980).

B. C. Dhage (1984) introduced the concept of D-metric in order to translate results from usual metric space to D-metric space. Mustafa and Sims (2003) showed that most of the results concerning D-metrics are incorrect. Mustafa and Sims (2006) took a different approach and introduced the notion of G-metric. Until now, many mathematicians are interested in discussing the concept.

In this paper, we will define metrics in the G-metric space. this is the first time that a G-metric space can be seen as a metric space. this means that the G-metric space and the metric space are equivalent. We also develop the theory for this metrics and obtain some fixed point theorems.

metric; fixed point theorem; G-metric.