Abstract: In this paper, we introduce the notions of commutating, compatibility and weakly compatible mappings on digital metric spaces. Using this concept we prove some common fixed point theorems for a pair of self-maps on a digital metric space. We also give an example of a pair of self-maps which is weakly compatible but not compatible and give another example in support of our main result.
Keywords: Digital Image, digital Metric Space, Adjacency relation, Commuting mappings, Compatibility mappings, Weakly Compatible Mappings, Coincidence Point. 2010 MSC: 47H10, 54E35, 68U10