\(\varphi\)-pairs and common fixed points in cone metric spaces. (English) Zbl 1164.54031

Summary: In this paper, we introduce a contractive condition, called \(\varphi\)-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for \(\varphi\)-pairs. We also obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.


54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
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