Common Fixed Points of a Family of Commuting Mappings of Partially Ordered Sets / D. A. Podoprikhin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 5. P. 56-59 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 216-218].

The paper presents conditions providing the existence of a common fixed point of a family of commuting isotone multivalued mappings of a partially ordered set and the existence of the minimal element in the set of common fixed points. Additional conditions that guarantee the existence of the least element in that point set are also presented. Relations of the obtained results to well-known fixed point theorems are discussed.

Key words: common fixed points, partially ordered set, isotone mapping, commuting family, multivalued mapping.

№ 5/2016