Dini derivative

The upper Dini derivativeMathworldPlanetmath of a continuous functionMathworldPlanetmath, f:𝐑𝐑, denoted by f+, is defined as


The lower Dini derivative, f-, is defined as


Remark: Sometimes the notation D+f(t) is used instead of f+(t), and D-f(t) is used instead of f-(t).

Remark: Like conventional derivatives, Dini derivatives do not always exist.

If f is defined on a vector space, then the upper Dini derivative at t in the direction d is denoted


If f is locally LipschitzPlanetmathPlanetmath then D+f is finite. If f is differentiableMathworldPlanetmathPlanetmath at t then the Dini derivative at t is the derivative at t.

Title Dini derivative
Canonical name DiniDerivative
Date of creation 2013-03-22 13:57:00
Last modified on 2013-03-22 13:57:00
Owner lha (3057)
Last modified by lha (3057)
Numerical id 11
Author lha (3057)
Entry type Definition
Classification msc 47G30