Purchase Solution

Proof with convex sets

Not what you're looking for?

Ask Custom Question

A Theorem states: Convex Sets are closed under convex combinations. That is, if C is a convex set, and if x1,x2,...,xm belongs to C then for all non-negative real numbers %1,%2,...,%m are non-negative real numbers such that $1+$2+....+$m=1, we have
$1x1 + $2x2 + ... + $mxm belonging to C.

Furthermore, I want to prove that if x1,x2,x3,x4 are in the convex set C, and if $1,$2,$3,%4 are non-negative real numbers such that $1+$2+$3+$4=1 then $1x1+$2x2+$3x3+$4x4 belonging to C
(please give full proof)

Purchase this Solution
Solution Summary

This is a proof regarding convex sets and non-negative numbers

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Convex and Compact Sets and the Implicit Function Theorem

    This solution provides the proof for the convex and compact sets in an attached Word document.

  • Interior of proper angles

    Thus the interior of any proper angle is a convex set. This is a proof regarding convex sets and interior of proper angles.

  • Norms and Bounded Sets

    Consider non-empty open sets B C V with the following properties: (a) B is bounded and convex (contains the line segment through any two of its points); (b) If VEB,then there is a number t0>0 for which tv EB......

  • Connected Convex Subsets

    (c) Prove that every convex subset of Rk is connected Proof: We should clarify the definition of separated sets. We say and are separated, if the distance of and is .

  • Convex Sets and Linear Transformations

    Therefore the set x = Ay is convex This solution looks at the properties that make convex sets.

  • Unit ball

    For any with , . Then . Thus . Hence is a balanced set. Third, I claim that is an absorbing set. For any , if , then ; if , we consider , then . Thus is an absorbing set. Therefore, is a convex, balanced and absorbing set.

  • Convex Hull : Closed and Compact Sets

    It's helpful to draw a picture of this... the convex hull basically consists of the strip of all (x,y) with 0 < y <= 1 and x>=0 together with the point (0,0). Convex Hulls, Closed and Compact Sets are investigated using the Cartheodory Theorem.

  • Functional analysis proof

    200838 Basic Functional Analysis I've attached the problem I need assistance with. Thanks! Prove that A is convex and absorbing and.... Hello I have attached solution for the problem 4. This is a proof regarding a convex and absorbing set.

  • Weak closures

    Proof. The sets of the form where all are in X*, make a base for the weak neighborhoods of x . Thus there exists (for some n) and such that is contained in U .

View More Related Solutions