Bohr's inequality revisited

TL;DR

This paper reviews and extends various forms of Bohr's inequality, including operator versions, eigenvalue extensions, and related inequalities in Hilbert spaces, offering new approaches and generalizations.

Contribution

It introduces new generalizations and approaches to Bohr's inequality, including operator and eigenvalue extensions, enriching the theoretical framework.

Findings

Several significant results on Bohr's inequality are surveyed.

New generalizations of Bohr's inequality are presented.

Extensions to Hilbert space operators and eigenvalues are discussed.

Abstract

We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality. An eigenvalue extension of Bohr's inequality is discussed as well.