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

In this paper, we introduce the metric d G 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 , d G ) . 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 , d G ) .