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On the conditions of existence coincidence points for mapping in partially ordered spaces

Annotation

A.V. Arutyunov, E.S. Zhukovskiy, S.E. Zhukovskiy studied the coincidence points for mappings of partially ordered spaces in particular, it was proved that an covering and monotone mapping, acting from a partially ordered space (X,≽_X ) to a partially ordered space (Y,≽_Y ), have a coincidence point. It is shown that the conditions of this assertion can be weakened: the binary relation ≽_Y should not be in order. We give an appropriate result and demonstrate an example of mappings satisfying its conditions, but to which the results of the cited work are not applicable.

Keywords

coincidence point; partially ordered space; covering map; monotonic mapping

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DOI

10.20310/1810-0198-2018-23-121-10-16

UDC

517.988.63, 512.562

Pages

10-16

References

1. Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. Coincidence points principle for mappings in partially ordered spaces. Topology and Its Applications, 2015, vol. 179, no. 1, pp. 13-3. DOI: 10.1016/j.topol.2014.08.013. 2. Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. Coincidence points principle for set-valued mappings in partially ordered spaces. Topology and Its Applications, 2016, vol. 201, pp. 330-343. DOI: 10.1016/j.topol.2015.12.044. 3. Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. O tochkakh sovpadeniya otobrazheniy v chastichno uporyadochennykh prostranstvakh [Coincidence points of set-valued mappings in partially ordered spaces]. Doklady Akademii nauk – Doklady Mathematics, 2013, vol. 88, no. 3, pp. 727-729. (In Russian). 4. Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. Tochki sovpadeniya mnogoznachnykh otobrazheniy v chastichno uporyadochennykh prostranstvakh [On coincidence points of mappings in partially ordered spaces]. Doklady Akademii nauk – Doklady Mathematics, 2013, vol. 88, no. 3, pp. 710-713. (In Russian). 5. Arutyunov A.V. Nakryvayushchie otobrazheniya v metricheskikh prostranstvakh i nepodvizhnye tochki [Covering mappings in metric spaces and fixed points]. Doklady Akademii nauk – Doklady Mathematics, 2007, vol. 76, no. 2, pp. 665-668. (In Russian). 6. Zhukovskiy E.S. Ob uporyadochenno nakryvayushchikh otobrazheniyakh i neyavnykh differentsial'nykh neravenstvakh [On ordered-covering mappings and implicit differential inequalities]. Differential Equations, 2016, vol. 52, no. 12, pp. 1539-1556. (In Russian). 7. Zhukovskiy E.S. Ob uporyadochenno nakryvayushchikh otobrazheniyakh i integral’nykh neravenstvakh tipa Chaplygina [About orderly covering mappings and Chaplygin’s type integral inequalities]. Algebra i analiz – St. Petersburg Mathematical Journal, 2018, vol. 30, no. 1, pp. 96-127. (In Russian).

Received

2018-01-15

Section of issue

Scientific articles

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