MHB Meaning of Cosx - Contraction, Contractive, Nonexpansive or Lipschtzian?

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The discussion centers on the mathematical properties of the cosine function, specifically whether it is classified as contraction, contractive, nonexpansive, or Lipschitzian. Participants seek clarification on the definitions of these terms, particularly the distinctions between contraction and contractive. There is an emphasis on understanding Lipschitz continuity and its relevance to the cosine function. The conversation encourages sharing prior attempts to address these concepts. Overall, the thread aims to clarify the nature of cos(x) in mathematical terms.
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what is cosx ? contraction, contractive, nonexpansive or lipschtzian...which is true ?
 
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ozkan12 said:
what is cosx ? contraction, contractive, nonexpansive or lipschtzian...which is true ?

Hi ozkan12,

Perhaps I am not getting your question clearly; are you trying to figure out what is meant by "cosx" ? For one, it might mean the cosine of x.
 
ozkan12 said:
what is cosx ? contraction, contractive, nonexpansive or lipschtzian...
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?
 

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