Abstract:
<jats:p>A strong Schwarzian derivative is defined, and it is shown that the convolution of a function with a map from an interval into itself having negative strong Schwarzian derivative is a function with negative Schwarzian derivative. Such convolutions have<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$0$" id="E1"><mml:mn>0</mml:mn></mml:math>as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.</jats:p>
Description:
<jats:p>A strong Schwarzian derivative is defined, and it is shown that the convolution of a function with a map from an interval into itself having negative strong Schwarzian derivative is a function with negative Schwarzian derivative. Such convolutions have<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$0$" id="E1"><mml:mn>0</mml:mn></mml:math>as a stable periodic point and at most one other stable periodic orbit in the interior of the domain.</jats:p>