Popularizations And Applications Of Cauchy-Schwarz Inequality

Cauchy-Schwarz inequality is one of the most general inequalities in mathematical area. In this paper, we conclude the basic forms of Cauchy-Schwarz inequality in different mathematical areas and provide their proof, discuss their inner connection. A systematic review of the generalization of Cauchy-Schwarz inequality is given. The use of integral Cauchy-Schwarz inequality is generalized to the multivariate function, and with some existing constraints, a new improved inequality is derived from Cauchy-Schwarz inequality. Through a series of examples, it explains some basic ways of how to use Cauchy-Schwarz inequality to prove inequality,to calculate maximum and minimum, and solving equations.