Variational Principles in Fang Uniform Spaces

TL;DR

This paper explores the relationships between various variational principles in Fang uniform spaces, establishing their equivalences and providing new proofs for known principles.

Contribution

It demonstrates the equivalence of the Zhu-Li Variational Principle with classical principles and offers a direct proof of Hamel's Variational Principle's equivalence with Ekeland's.

Findings

ZLVP is equivalent to BB and EVP

The paper provides a direct proof of HVP's equivalence with EVP

Results unify different variational principles in Fang uniform spaces

Abstract

The vectorial Zhu-Li Variational Principle (ZLVP) in Fang uniform spaces is in the logical segment between the Brezis-Browder ordering principle (BB) and Ekeland's Variational Principle (EVP); hence, it is equivalent with both BB and EVP. In particular, the conclusion is applicable to Hamel's Variational Principle (HVP). Finally, a proof of [HVP equivalent with EVP] is provided, by means of a direct approach.