A new approach to fixed point theorems on G-metric spaces

In this paper, we introduce the metric dG on a G-metric space (X,G) and use this notion to show that many contraction conditions for maps on the G-metric space (X,G) reduce to certain contraction conditions for maps on the metric space (X,dG). As applications, the proofs of many fixed point theorems for maps on the G-metric space (X,G) may be simplified, and many fixed point theorems for maps on the G-metric space (X,G) are direct consequences of preceding results for maps on the metric space (X,dG).