Abel inequality

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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.

How to Cite This Entry:
Abel inequality. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article