Abstract
In this paper we utilize the notion of Ω-distance in the sense of Saadati et al. (Math. Comput. Model. 52:797-801, 2010) to construct and prove some fixed and coupled fixed point theorems in a complete G-metric space for a nonlinear contraction. Also, we provide an example to support our results.
Highlights
The concept of G-metric space was introduced by Mustafa and Sims [ ]
In [ ], the author proves a common fixed point theorem for two self-mappings verifying a contractive condition of integral type in G-metric spaces
Fixed point theorems for mappings with a contractive iterate at a point are formulated in [ ] and in [ ]
Summary
The concept of G-metric space was introduced by Mustafa and Sims [ ]. Many authors constructed fixed point theorems in G-metric spaces. In [ ] and [ ], common fixed points results for mappings which satisfy the generalized (φ, ψ)-weak contraction are obtained. In [ ], the author proves a common fixed point theorem for two self-mappings verifying a contractive condition of integral type in G-metric spaces.
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