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

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SUMMARY

The discussion centers on the mathematical function "cos(x)" and its classification as either contraction, contractive, nonexpansive, or Lipschitzian. Participants clarify that "cos(x)" refers to the cosine function, which is Lipschitz continuous due to its bounded derivative. The terms contraction and contractive are differentiated, with emphasis on the definition of nonexpansive functions, which maintain distance. Overall, the consensus is that "cos(x)" is Lipschitzian, and understanding these classifications is essential for further mathematical exploration.

PREREQUISITES
  • Understanding of Lipschitz continuity
  • Knowledge of nonexpansive functions
  • Familiarity with contraction mappings
  • Basic trigonometric functions, specifically cosine
NEXT STEPS
  • Research the properties of Lipschitz continuous functions
  • Study the definitions and examples of nonexpansive functions
  • Explore contraction mappings in metric spaces
  • Learn about the implications of cosine function behavior in calculus
USEFUL FOR

Mathematicians, students studying real analysis, and anyone interested in the properties of trigonometric functions and their classifications in functional analysis.

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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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