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Existence of coincidence point under generalized Geraghty-type contraction with application. (English) Zbl 1490.54064

Summary: We establish coincidence point theorem for \(S\)-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings \(F,G:X^2\to X\). As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

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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