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For each of the following sets, prove whether they are convex or not. 1. Given a collection of n = N convex sets {S}"ï±1, S := 2. Given p > 0, S := {x = Rd : ||x||₂ = 1}. € i=1' ±1 Si. i=1 3. Given p≥ 1, S := {{a¡};£1, a¡ € R : (Σºº1₁ |ai|P)½³ < ∞0}.

For each of the following sets, prove whether they are convex or not. 1. Given a collection of n = N convex sets {S}"ï±1, S := 2. Given p > 0, S := {x = Rd : ||x||₂ = 1}. € i=1' ±1 Si. i=1 3. Given p≥ 1, S := {{a¡};£1, a¡ € R : (Σºº1₁ |ai|P)½³ < ∞0}.

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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For each of the following sets, prove whether they are convex or not. 1. Given a collection of n = N convex sets {S}"ï±1, S := 2. Given p > 0, S := {x = Rd : ||x||₂ = 1}. € i=1' ±1 Si. i=1 3. Given p≥ 1, S := {{a¡};£1, a¡ € R : (Σºº1₁ |ai|P)½³ < ∞0}.
Transcribed Image Text:For each of the following sets, prove whether they are convex or not. 1. Given a collection of n = N convex sets {S}"ï±1, S := 2. Given p > 0, S := {x = Rd : ||x||₂ = 1}. € i=1' ±1 Si. i=1 3. Given p≥ 1, S := {{a¡};£1, a¡ € R : (Σºº1₁ |ai|P)½³ < ∞0}.
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