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Convex sequence

From Encyclopedia of Mathematics
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A sequence of real numbers , satisfying the condition

(*)

Putting

condition (*) may be written as

The geometrical meaning of condition (*) is that the broken line in the ()-plane with corners at the points , is convex. If the sequence is both convex and bounded, then:

1) it does not increase and thus converges to a finite limit;

2) ;

3) .

If is a convex function (of a real variable) for , the sequence , is convex.

How to Cite This Entry:
Convex sequence. L.D. Kudryavtsev (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convex_sequence&oldid=16907
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098