Definition of "equibounded"

equibounded

adjective
not comparable
1. (mathematics, of a family of functions) Having the property that there exists a positive number M such that for all functions f in the family of functions F defined on X, |f(x)| ≤ M for all x in X.
  Quotations
  The stability is shown to be uniform with respect to the singular parameter or the solutions are shown to be equibounded.
  1994, Stability & Applied Analysis of Continuous Media, volume 3, page 277
  An important example of such a semigroup in infinite dimensional Hilbert space is the weak operator closed monothetic semigroup generated by a linear operator with equibounded iterates.
  2011, M. A. Kaashoek, T. T. West, Locally Compact Semi-Algebras, page 8