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A function f : X → Y is called locally Lipschitz if at each x ∈ X , there exists such that the restriction of f to the open ball of radius δ and center x (which we denote by S d ( x , δ ) ) is Lipschitz: Of course the radius δ may be dependent on x: consider f : ( 0 , ∞ ) → ( 0 , ∞ ) defined by f ( x ) = 1 / x .
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Oct 8, 2013 · A function f:A→B is locally xyz if every point x∈A has a neighbourhood U such that f|U is xyz. (For things like local homeomorphisms, ...
In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions.
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+ function can be LOCALLY Lipschitz if there exists a positive constant. L that satisfies this condition in a specific raghborhood. + additionally, this can ...
Mar 16, 2020 · Lipschitz means that there's a constant bound on how fast the function can change. 1/x is Lipschitz on (1, 2), for example (the absolute ...
We refer to M as a Lipschitz constant for f. A sufficient condition for f = (f1,...,fd) to be a locally Lipschitz continuous function of x = ( ...
Definition 2.4 A locally Lipschitz function f : X → R is said to be regular at u ∈ X, if the one-sided directional derivative f (u; v) exists for all v ...
Mar 3, 2022 · Function f is locally Lipschitz on W ⊂ X if for each w ∈ W there exists open W0 ⊂ W containing w such that f is Lipschitz on W0. Theorem 1.
Lipschitz condition (1.1) is global; it requires control over each pair of points a, b in A. Sometimes we only have local information.
The purpose of this note is to investigate how often a locall schitz function must be regular, and make connections to the possible m density behaviour of ...