An equality in mathematical analysis, established by V.Ya. Bunyakovskii  for square-integrable functions and :
This inequality is analogous to Cauchy's algebraic inequality
The Bunyakovskii inequality is also known as the Schwarz inequality; however, Bunyakovskii published his study as early as 1859, whereas in H.A. Schwarz' work this inequality appeared as late as 1884 (without any reference to the work of Bunyakovskii).
|||W. [V.Ya. Bunyakovskii] Bounjakowsky, "Sur quelques inegalités concernant les intégrales aux différences finis" Mem. Acad. Sci. St. Petersbourg (7) , 1 (1859) pp. 9|
In Western literature this inequality is often called the Cauchy inequality, or the Cauchy–Schwarz inequality. Its generalization to a function in and a function in , , is called the Hölder inequality.
Cauchy's algebraic inequality stated above holds for real numbers , . For complex numbers , , it reads
It has a generalization analogous to the Hölder inequality.
|[a1]||W. Rudin, "Principles of mathematical analysis" , McGraw-Hill (1953)|
Bunyakovskii inequality. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bunyakovskii_inequality&oldid=29421