Existence of Fixed Point Results in G-Metric Spaces

The study of metric fixed point theory has been researched extensively in the past decades, since fixed point theory plays a major role in mathematics and applied sciences, such as optimization, mathematical models, and economic theories. Different mathematicians tried to generalize the usual notion of metric space X, d such as Gähler 1, 2 andDhage 3–5 to extend knownmetric space theorems inmore general setting, but different authors proved that these attempts are unvalid for detail see 6–8 . In 2005, Mustafa and Sims introduced a new structure of generalized metric spaces see 9 , which are calledG-metric spaces as generalization of metric space X, d , to develop and introduce a new fixed point theory for various mappings in this new structure. The Gmetric space is as follows.