5. Let (α1,α2,...,ân) and (b1,b2,...,bn) be two n-tuples 1 1 bers and let p, q be two positive real numbers such that + of indices is called a pair of conjugate indices.) Then the inequality p q 1/p P |Σα|= (Σ11)" (Σ11) j=1 j=1 j=1 19 1/9 " = 1. (

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 78E
icon
Related questions
Question
5. Let (a₁, a2,...‚an) and (b₁,b2,...,bn) be two n-tuples of real
1 1
numbers and let p, q be two positive real numbers such that + = 1. (Such a
pair of indices is called a pair of conjugate indices.) Then the inequality
P 9
n
n
1/q
n
1/p
Σªb;|≤ ([«;l”)¹([Þ;")¹,
j=1
j=1
j=1
holds. Moreover this is an equality if and only if |aj|P = X|bj|ª, 1 ≤ j ≤ n, for
some real constant X.
Transcribed Image Text:5. Let (a₁, a2,...‚an) and (b₁,b2,...,bn) be two n-tuples of real 1 1 numbers and let p, q be two positive real numbers such that + = 1. (Such a pair of indices is called a pair of conjugate indices.) Then the inequality P 9 n n 1/q n 1/p Σªb;|≤ ([«;l”)¹([Þ;")¹, j=1 j=1 j=1 holds. Moreover this is an equality if and only if |aj|P = X|bj|ª, 1 ≤ j ≤ n, for some real constant X.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage