The least constant for which the previous inequality holds, is called the Lipschitz constant of . The space of Lipschitz continuous functions is often denoted by .
Clearly, every Lipschitz continuous function is continuous.
More generally, one says that a mapping satisfies a Lipschitz condition of order if there exists a real constant such that
Functions which satisfy this condition are also called Hölder continuous or -Hölder. The vector space of such functions is denoted by and hence .
|Date of creation||2013-03-22 11:57:48|
|Last modified on||2013-03-22 11:57:48|
|Last modified by||paolini (1187)|