Generalized Cauchy–Bunyakovsky–Schwarz inequalities and their applications

M. Hosseini^a, R. Nuraei^a, M. Shah Hosseini<sup>b

a</sup> Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
^b Department of Mathematics, Islamic Azad University, Shahr-e-Qods Branch, Tehran, Iran

Abstract: In this article, we present generalized improvements of certain Cauchy–Bunyakovsky–Schwarz type inequalities. As applications of our results, we provide improvements of some numerical radius inequalities for Hilbert space operators. Finally, we obtain certain numerical radii of Hilbert space operators involving geometrically convex functions.

Keywords: Cauchy–Bunyakovsky–Schwarz inequality, numerical radius, operator norm.

MSC: Primary 47A12, 47A30, 15A60, 47A63; Secondary 47A30, 15A60, 47A63

Received: 09.10.2023
Revised: 17.03.2024
Accepted: 23.03.2024

DOI: 10.4213/faa4164

 English version: Functional Analysis and Its Applications, 2024, 58:3, 313–325

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