Geodesic
On idempotent elements of semigroup of increasing monotonous mappings
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 27-33

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In some special classes of ordered topological spaces we characterize roundings as extreme points of set of non increasing isotonic mappings, and establish their stability in Hyers–Ulam sense. 
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     author = {A. L. Kryukova},
     title = {On idempotent elements of semigroup of increasing monotonous mappings},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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A. L. Kryukova. On idempotent elements of semigroup of increasing monotonous mappings. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 27-33. http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a3/