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Remarks on some recent coupled coincidence point results in symmetric \(G\)-metric spaces. (English) Zbl 1300.54081
Summary: We use a method of reducing coupled coincidence point results in (ordered) symmetric \(G\)-metric spaces to the respective results for mappings with one variable, even obtaining (in some cases) more general theorems. Our results generalize, extend, unify, and complement recent coupled coincidence point theorems in this frame, established by Y. Cho et al. [Fixed Point Theory Appl. 2012, Article ID 8, 14 p. (2012; Zbl 1348.54044)], H. Aydi et al. [Math. Comput. Modelling 54, No.  9–10, 2443–2450 (2011; Zbl 1237.54043)], and B. S. Choudhury and P. Maity [Math. Comput. Modelling 54, No.  1–2, 73–79 (2011; Zbl 1225.54016)]. Also, by using our method, several recent tripled coincidence point results in ordered symmetric \(G\)-metric spaces can be reduced to the coincidence point results with one variable.

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