Description:
<jats:title>Abstract</jats:title><jats:p>We derive a simple sufficient condition for a point <jats:italic>a</jats:italic>∈<jats:italic>S</jats:italic>⊂<jats:italic>X</jats:italic> be a local minimum of <jats:italic>f: X → R</jats:italic> on <jats:italic>S</jats:italic>. This condition is of the first order in its nature and takes into account the derivative (or some generalization of it) in a neighborhood of <jats:italic>a.</jats:italic> Applications like a sufficient condition for (<jats:italic>a, b</jats:italic>)∈ <jats:italic>S</jats:italic> × <jats:italic>T</jats:italic> ⊂ <jats:italic>X</jats:italic> × <jats:italic>Y</jats:italic> be a saddle‐point of a bivariate function <jats:italic>f: X</jats:italic> × <jats:italic>Y ⊂ <jats:bold>R</jats:bold></jats:italic> are also proposed.</jats:p>