MHB Fixed Point Theory: Lipschitz or Contraction?

ozkan12
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I see that if a mapping is contraction then it is contractive then it is nonexpensive and then it is lipschtiz...so, which class of mapping is general ? lipschitz or contraction ? which one ? thank you for your attention :)
 
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Contraction is a special case of Lipschitz continuous functions, namely, with Lipschitz constant $K$ satisfying $0\le K<1$.
 
so, lipschitz mappings are more general than contraction ?
 
ozkan12 said:
so, lipschitz mappings are more general than contraction ?
Yes.
 
ok. thanks a lot :)
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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