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            Abstract
 
  The property of so-called uniform covering is proved for a family of linear operators generated
  by a differential equation linear with respect to functional parameters. Using this fact, a uniform
  estimate of the distance to the level set of a nonlinear operator is obtained on a broader set than
  a neighborhood of the examined point in a Banach space. This allows to prove an approximation
  theorem for a system with sliding mode controls and endpoint state constraints.


  Key words:
  nonlinear operator, covering, weak-* topology, sliding modes.
 
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