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Basic inequalities A function : I R defined on an interval I R is convex if for all integer
 

Summary: Basic inequalities
N.A.
07
A function : I R defined on an interval I R is convex if for all integer
n 2:
n
j=1
tj = 1, t1, . . . , tn 0, a1, . . . , an I =


n
j=1
tjaj


n
j=1
tj (aj) .
By induction, is convex iff the inequality above holds for n = 2.
Jensen's inequality.1

  

Source: Arcozzi, Nicola - Dipartimento di Matematica, UniversitÓ di Bologna

 

Collections: Mathematics