An equality in mathematical analysis, established by V.Ya. Bunyakovskii [1] 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).

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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.

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