An estimate for the sum of products of two numbers. If sets of numbers and are given such that the absolute values of all sums , , are bounded by a number , i.e. , and if either or , , then
If the are non-increasing and non-negative, one has the simpler estimate:
Abel's inequality is proved by means of the Abel transformation.
Abel inequality. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Abel_inequality&oldid=18342