Need help with this question. Thank you :) a) Restate Definition 3.6, and check by elementary computations that themapping g: R → R given by g(x) = x/2is a contraction on the closed set R, andpossesses the unique fixed point x* = 0. Definition 3.6: Lipschitz property and contractionsLet DC Rd, and fix a norm ||· || : Rd → R+.a) A function f : D → Rd is called L-Lipschitz with L € [0, ∞) if||f(x) = f(y)|| ≤L||xy|| Vr, y = D.It is called Lipschitz if it is L-Lipschitz for some L € [0, ∞).b) A function f : D → D is called a contraction if it is L-Lipschitz forsome L € [0, 1).

What is Lipschitz Function: A function is referred to as Lipschitz function if the norm of the…

Answered: a) Restate Definition 3.6, and check by…

a) Restate Definition 3.6, and check by elementary computations that the mapping g: R → R given by g(x) = x/2 is a contraction on the closed set R, and possesses the unique fixed point x* = 0.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

100%

Need help with this question. Thank you :)

a) Restate Definition 3.6, and check by elementary computations that the
mapping g: R → R given by g(x) = x/2
is a contraction on the closed set R, and
possesses the unique fixed point x* = 0.

Definition 3.6: Lipschitz property and contractions
Let DC Rd, and fix a norm ||· || : Rd → R+.
a) A function f : D → Rd is called L-Lipschitz with L € [0, ∞) if
||f(x) = f(y)|| ≤L||xy|| Vr, y = D.
It is called Lipschitz if it is L-Lipschitz for some L € [0, ∞).
b) A function f : D → D is called a contraction if it is L-Lipschitz for
some L € [0, 1).

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