New refinements of the Cauchy–Bunyakovsky inequality

Abstract

This paper presents new refinements on the integral form of Cauchy–Schwartz inequality known as Cauchy–Bunyakovsky inequality. It is proved that when we possess a weighted sum of a set of Cauchy–Bunyakovsky inequalities, there are two forms of refinements enhancing the precision of the original inequality. The superiority of one refinement over the other depends on the problem in which the presented theorem is utilized.