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ozkan12
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what is cosx ? contraction, contractive, nonexpansive or lipschtzian...which is true ?
ozkan12 said:what is cosx ? contraction, contractive, nonexpansive or lipschtzian...which is true ?
It would also be nice if you remind us the definition of some of these concepts. Lipschitz continuous function is a well-known thing, but nonexpansive is less so, I believe. And what is the difference between contraction and contractive? Finally, what have you tried to answer your question?ozkan12 said:what is cosx ? contraction, contractive, nonexpansive or lipschtzian...
"Cosx" is a mathematical notation for the cosine function, which is a trigonometric function that relates the lengths of the sides of a right triangle to the measure of its angles. It is defined as the ratio of the adjacent side to the hypotenuse of the triangle.
In mathematics, a contraction is a function that maps a metric space to itself and reduces the distance between any two points in the space. In other words, a contraction shrinks the space and brings points closer together.
A function is considered contractive if it satisfies the condition that the distance between the images of any two points in the space is always less than the distance between the two original points. This means that the function "contracts" the space and brings points closer together.
While a contractive function reduces the distance between points in a space, a nonexpansive function preserves the distance between points. In other words, a nonexpansive function does not "stretch" the space in any way.
A function is considered Lipschitzian if it satisfies the Lipschitz condition, which states that the distance between the images of any two points in the space is always bounded by a constant multiple of the distance between the two original points. This means that the function is not allowed to "stretch" the space too much.