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We  prove some fixed point results for mapping satisfying sufficient conditions on complete G-metric space, also we showed  that if the G-metric space (X,G) is symmetric, then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space (X,dG), where (X,dG) is the usual metric space which defined from the G-metric space (X,G)

Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces