This paper concerns with exact and approximate Ekeland variational principles for vector-valued functions and bifunctions that are derived via linear and nonlinear scalarization processes by an approximate scalar formulation of the Ekeland variational principle and a revised version of Dancs–Hegedüs–Medvegyev's fixed point theorem. Both results are also interesting in themselves and involve really mild assumptions. As a result, the obtained Ekeland variational principles improve some recent results in the literature since weaker assumptions are required.

中文翻译：

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精确和近似向量 Ekeland 变分原理

本文涉及矢量值函数和双函数的精确和近似 Ekeland 变分原理，这些函数和双函数是通过 Ekeland 变分原理的近似标量公式和 Dancs–Hegedüs–Medvegyev 不动点定理的修订版通过线性和非线性标量化过程导出的。这两个结果本身也很有趣，并且涉及非常温和的假设。因此，获得的 Ekeland 变分原理改进了文献中的一些最新结果，因为需要更弱的假设。