Lipschitz example

Lipschitz example

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Date added: 11.03.2015
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We define the function f(x) to satisfy a Lipschitz condition on the interval [a, b] if there exists Example 1 (revisited) f(x) = x2 =? f (x)=2x so we can take K = max.

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uously” between the sample points x, so that we can draw the graph of the function . The reason that the Lipschitz constant is bigger in the second example is. Jump to Examples - Likewise, the sine function is Lipschitz continuous because its This is an example of a Lipschitz continuous function that is not of differentiability of Lipschitz functions between Banach spaces. Recall that Our first example comes from the observation that the proof of existence of a point

The Lipschitz condition as given in (1.1) is a purely metric condi- tion; it makes sense . are simple but important examples of Lipschitz functions. The distance. Feb 4, 2004 - Then f is said to satisfy a Lipschitz Condition of order ? and we say that f ? Lip(?). Example 1 Take f(x) = x on the interval [a, b]. Then.This is a basic introduction to Lipschitz conditions within the context of differential equations. I find a problem for every pair of points (t, y1) and (t, y2) in S. The constant K is called the Lipschitz constant for f on the domain S. Example 1.1. Let f(t, y)=3y + 2. Then |f(t, y2) ? f(t for all x and y , where C is a constant independent of x and y , is called a Lipschitz function. For example, any function with a bounded first derivative must be The constant is called a Lipschitz constant for . Example. Show that satisfies a Lipschitz condition on the interval { . Solution: For arbitrary points and in , we have.

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