Fixed Point Theory for Contractive Mappings Satisfying -Maps in G-Metric Spaces

The fixed point theorems in metric spaces are playing a major role to construct methods in mathematics to solve problems in applied mathematics and sciences. So the attraction of metric spaces to a large numbers of mathematicians is understandable. Some generalizations of the notion of a metric space have been proposed by some authors. In 2006, Mustafa in collaboration with Sims introduced a new notion of generalized metric space called Gmetric space 1 . In fact, Mustafa et al. studied many fixed point results for a self-mapping in G-metric space under certain conditions; see 1–5 . In the present work, we study some fixed point results for self-mapping in a complete G-metric space X under some contractive conditions related to a nondecreasing map φ : 0, ∞ → 0, ∞ with limn→ ∞φ t 0 for all t ∈ 0, ∞ .