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An exercise in functional analysis. The professor during last lecture said that to make sure a function can be used as a norm the most difficult part is to prove that the property of triangle inequality works. One way to prove this is to prove that the function is concave (not convex). So, the task is to prove or disprove that the following function is concave (not convex) and therefore the triangle inequality is satisfied: 4 n(x) = Vx +x, x = (x,x, ) E R

An exercise in functional analysis. The professor during last lecture said that to make sure a function can be used as a norm the most difficult part is to prove that the property of triangle inequality works. One way to prove this is to prove that the function is concave (not convex). So, the task is to prove or disprove that the following function is concave (not convex) and therefore the triangle inequality is satisfied: 4 n(x) = Vx +x, x = (x,x, ) E R

Advanced Engineering Mathematics
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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An exercise in functional analysis. The professor during last lecture said that to make sure a function can be used as a norm the most difficult part is to prove that the property of triangle inequality works. One way to prove this is to prove that the function is concave (not convex). So, the task is to prove or disprove that the following function is concave (not convex) and therefore the triangle inequality is satisfied: 4 4 n(x) = Vx +x, x= (x.x, ) e R?
Transcribed Image Text:An exercise in functional analysis. The professor during last lecture said that to make sure a function can be used as a norm the most difficult part is to prove that the property of triangle inequality works. One way to prove this is to prove that the function is concave (not convex). So, the task is to prove or disprove that the following function is concave (not convex) and therefore the triangle inequality is satisfied: 4 4 n(x) = Vx +x, x= (x.x, ) e R?
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