Hölder’s and Minkowski’s inequalities
Hölder’s and Minkowski’s inequalities

Summary/Abstract: In the middle of the 19th century, the German mathematician H. A. Schwarz (1843–1921) and the Russian mathematician V. Y. Bunyakovsky (1804–1869) proved independently an inequality that is known in the literature as Cauchy–Bunyakovsky–Schwarz inequality. Later, the German mathematician O. Hölder (1859–1937) proved an inequality that generalizes Cauchy–Bunyakovsky–Schwarz inequality and is known under his name.Another important inequality was proved by the German mathematician H. Minkowski (1864–1909). In the literature this inequality is known under his name. All these inequalities are considered in the present paper. Their proofs will be based on the concept of a convex function and Jensen’s inequality.

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