Elementary Proofs of Common Inequalities Using a Generic Symmetric Recurrence Method
Year: 2025
Type: article
Abstract: This work introduces a variation on Augustin-Louis Cauchy’s classical proof of the arithmetic–geometric mean (AM–GM) inequality as presented in his 'Cours d’analyse de l’École Royale Polytechnique'. While replacing Cauchy’s forward–backward induction with a recurrence-based argument, it retains and systematizes the nested symmetric algebraic structure that underlies the latter part of his original development. This symmetry-based approach extends naturally to other canonical inequalities, including Jensen’s, Minkowski’s, and — via mild algebraic elaboration — Hölder’s inequality.
Author: Ko, Doyoung
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6968075445
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