11 - Algebraic Inequalities

Abstract

This chapter discusses algebraic inequalities involving real numbers and complex numbers, followed by inequalities for sets of complex numbers. The algebraic inequalities involving real numbers include Lagrange's identity, Cauchy–Schwarz–Buniakowsky inequality, Minkowski's inequality, Hölder's inequality, Chebyshev's inequality, Arithmetic–geometric inequality, Carleman's inequality, and an inequality involving absolute values. Discussion on inequalities for sets of complex numbers covers complex Cauchy–Schwarz–Buniakowsky inequality, Complex Minkowski inequality, and complex Hölder inequality,