Gauge Brezis-Browder Principles and Dependent Choice

TL;DR

This paper demonstrates that the gauge Brezis-Browder Principle is equivalent to the Principle of Dependent Choices and Ekeland's Variational Principle, establishing a foundational link between these key mathematical concepts.

Contribution

It shows that the gauge Brezis-Browder Principle can be derived from the Principle of Dependent Choices and implies Ekeland's Variational Principle, revealing their equivalence.

Findings

Gauge Brezis-Browder Principle is obtainable from DC.

It implies Ekeland's Variational Principle.

Equivalence of these principles is established.

Abstract

The gauge Brezis-Browder Principle in Turinici [Bull. Acad. Pol. Sci. (Math.), 30 (1982), 161-166] is obtainable from the Principle of Dependent Choices (DC) and implies Ekeland's Variational Principle (EVP); hence, it is equivalent with both (DC) and (EVP). This is also true for the gauge variational principle deductible from it, including the one in Bae, Cho, and Kim [Bull. Korean Math. Soc. 48 (2011), 1023-1032].