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Existence of common fixed point for \(b\)-metric rational type contraction. (English) Zbl 1461.54066

Summary: The necessary conditions for existence of a common fixed point of two mappings satisfying generalized \(b\)-order contractive condition in the setting of a partially ordered \(b\)-complete \(b\)-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized \(b\)-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.

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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