Mathematics > Functional Analysis
[Submitted on 10 Jun 2023
(v1)
, last revised 6 Mar 2024 (this version, v2)]
Title: Group invariant variational principles
Title: 群不变变分原理
Abstract: In this paper we introduce a group invariant version of the wellknown Ekeland variational principle. To achieve this, we defne the concept of convexity with respect to a group and establish a version of the theorem within this framework. Additionally, we present several consequences of the group invariant Ekeland variational principle, including Palais-Smale minimizing sequences, the Br{\o}nsted-Rockafellar theorem, and a characterization of the linear and continuous group invariant functionals space. Moreover, we provide an alternative proof of the Bishop-Phelps theorem and proofs for the group-invariant Hahn-Banach separating theorems. Finally, we discuss some implications and applications of these results.
Submission history
From: Daniel Isert Sales [view email][v1] Sat, 10 Jun 2023 16:44:32 UTC (14 KB)
[v2] Wed, 6 Mar 2024 09:36:32 UTC (14 KB)
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