Puttinga = x-y, b = y-z in(1), we have x- z| s Vlx-y| + ly-lg + ele2-1.7> d(x,z) < d(x,y)+ d(y,z), y,Z e R.Hence disametriconR.2-1.6 Example: If (X,d) is a metric space, then showd'(x.Solu2d(x,y)1+2d(x,y)Since d is metric, so d(x, y) 20= 2d(x,y) >0d;(x,y) =is also a metric on X.

Given that (X, d) is a metric space. To show that d1x,y=2dx,y1+2dx,y is also a metric on X. There…

Answered: 2-1.6 Example: If (X,d) is a metric…

2-1.6 Example: If (X,d) is a metric space, then show that (z'x)p = 2d(x,y) 1+2d(x, y) is also a metric on X. d,(x,y) = Odl x v) >0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Puttinga = x-y, b = y-z in(1), we have x- z| s Vlx-y| + ly-
lg + ele
2-1.7
> d(x,z) < d(x,y)+ d(y,z), y,Z e R.Hence disametriconR.
2-1.6 Example: If (X,d) is a metric space, then show
d'(x.
Solu
2d(x,y)
1+2d(x,y)
Since d is metric, so d(x, y) 20= 2d(x,y) >0
d;(x,y) =
is also a metric on X.

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