Convex sequence
From Encyclopedia of Mathematics
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
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