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Abdeljawad (Fixed Point Theory Appl., 2013:19) introduced the concept of α-admissible for a pair of mappings. More recently Salimi et al. [Fixed Point Theory Appl., 2013:151] modified the notion of α-ψ-contractive mappings. In this paper we introduce the concept of an α-admissible map with respect to η and modify the α-ψ-contractive condition for a pair of mappings and establish common fixed point results for two, three, and four mappings in a closed ball in complete dislocated metric spaces. As an application, we derive some new common fixed point theorems for ψ-graphic contractions defined on dislocated metric space endowed with a graph as well as preordered dislocated metric space. Some comparative examples are constructed which illustrate the superiority of our results to the existing ones in the literature.

Common fixed point results for α-ψ-contractions on a metric space endowed with graph