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Discussion on “Multidimensional coincidence points” via recent publications. (English) Zbl 1471.54022

Summary: We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications [S. Dalal et al., ibid. 2014, Article ID 614019, 8 p. (2014; Zbl 1471.54026)] and [M. Imdad et al., J. Oper. 2013, Article ID 532867, 8 p. (2013; Zbl 1300.54069)] have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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