Algebraic Inequalities by Hayk Sedrakyan & Nairi Sedrakyan

Author:Hayk Sedrakyan & Nairi Sedrakyan
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Remark

We have obtained a very beautiful inequality (8.1). However, it turns out that this is one of the forms of the Cauchy–Bunyakovsky–Schwarz inequality. Indeed, making a change of variables and we obtain Cauchy–Bunyakovsky–Schwarz inequality .

Note that in order to prove certain inequalities the form (8.1) is more convenient than the classical form of Cauchy–Bunyakovsky–Schwarz inequality.

Example 8.1

Prove that where

Proof

Note that according to Lemma 1 (for ), we have

This ends the proof.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.