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Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications. (English) Zbl 1259.54024

Summary: In this paper, we establish fixed point theorems for contractive mappings on a metric space endowed with an amorphous binary relation. The presented theorems extend and generalize many existing results on metric and ordered metric spaces. We apply also our main result to derive fixed point theorems for cyclical contractive mappings.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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Full Text: Euclid