Handa, Amrish Existence of coincidence point under generalized Geraghty-type contraction with application. (English) Zbl 1490.54064 J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 27, No. 3, 109-124 (2020). 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. Cited in 2 Documents 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 Keywords:coincidence point; Geraghty-type contraction; \(S\)-non-decreasing mapping; \(O\)-compatible; generalized compatibility; integral equation PDFBibTeX XMLCite \textit{A. Handa}, J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 27, No. 3, 109--124 (2020; Zbl 1490.54064) Full Text: DOI