Geodesic
Common Fixed Points of Commuting Monotone Mappings
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 617-620

Voir la notice de l'article provenant de la source Cambridge University Press

We are concerned here with the existence of fixed or common fixed points of commuting monotone self-mappings of a partially ordered set into itself. Let X be a partially ordered set. A self-mapping ƒ of X into itself is called an isotone mapping if x ⩾ y implies ƒ(x) ⩾ ƒ(y). Similarly, a self-mapping ƒ of X into itself is called an antitone mapping if x ⩾ y implies ƒ(x) ⩽ ƒ(y). An element X0 ∈ X is called well-ordered complete if every well-ordered subset with x 0 as its first element has a supremum. An element x 0 ∈ X is called chain-complete if every non-empty chain C ⊆ X such that x ⩾ x 0 for all x ∈ C, has a supremum. X is called a well-ordered-complete semi-lattice if every non-empty well-ordered subset has a supremum. X is called a complete semi-lattice if every non-empty subset of X has a supremum. 
Wong, James S. W. Common Fixed Points of Commuting Monotone Mappings. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 617-620. doi: 10.4153/CJM-1967-054-4
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