Abstract:
We obtain criteria for equivalence, covariance, commutativity, and idempotent additivity of roundings in ordered topological spaces. For some special classes of spaces, we obtain the characterization of roundings as extreme points of the set of nonenlarging isotone mappings and prove their Hyers–Ulam stability. A functional model
of interval rounding is constructed.
Keywords:rounding, partially ordered topological space, extreme point, Hyers–Ulam stability.
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