Geodesic
On coincidence points for vector mappings
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 14-28

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For mappings acting in the product of metric spaces we propose a concept of vector covering. This concept is a natural extension of the notion of covering for mappings in metric spaces. The statements on the solvability of systems of operator equations are proved for the case when the left-hand side of an equation is a value of a vector covering mapping and the right-hand side is Lipschitzian vector mapping. In the scalar case the obtained statements are equivalent to the coincide point theorems by A. V. Arutyunov. As an application, we prove a statement on the existence of $n$-fold coincidence points and obtain estimates of the points. The sufficient conditions for $n$-fold fixed points existence, including the well-known theorems on double fixed point, follow from the obtained results.
Keywords: system of operator equations, vector covering mappings of metric spaces, coincidence points, $n$-fold fixed points. 
@article{IVM_2016_10_a2,
     author = {E. S. Zhukovskiy},
     title = {On coincidence points for vector mappings},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {14--28},
     publisher = {mathdoc},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_10_a2/}
}
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E. S. Zhukovskiy. On coincidence points for vector mappings. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 14-28. http://geodesic.mathdoc.fr/item/IVM_2016_10_a2/