Buniakovskii's Inequality

Buniakovskii’s Inequality 

one of the most important inequalities of mathematical analysis which asserts that

It was established by V. Ia. Buniakovskii. This inequality is analogous to the elementary algebraic Cauchy inequality

and can be obtained from the latter by proceeding to the limit. In mathematical literature Buniakovskii’s inequality is often erroneously called Schwarz’ inequality, named for H. A. Schwarz. However, Buniakovskii had published his work on inequalities in 1859, while the same inequality appeared in Schwarz’ work no earlier than 1884 (without reference to Buniakovskii).

REFERENCE

Buniakovskii, V. “Sur quelques inégalités concernant les intégrales ordinaires et les intégrales aux différences finies (Lu le 29 avril 1859).” Mémoires de l’ Académie des sciences de St. Pétersbourg, 7 série, 1859, vol. 1, no. 9.