再论Borwein-Preiss变分原理
Borwein-Preiss Variational Principle Revisited
摘要：
在这篇文章中，我们改进和稍微加强了度量空间版本的Borwein-Preiss变分原理，由于李，施，J。Appl.246，308-319（2000），阐明了Borwein，Zhu，Techniques of Variational Analysis，Springer（2005）中定理1和定理2.5.2的假设和结论，并简化了证明。我们的主要结果定理3是在度量空间中得到的。当归结到巴拿赫空间时（推论9），它沿几个方向扩展和加强了Borwein，Preiss，Trans.Amer.Math.Soc.303，517-527（1987）中建立的光滑变分原理。
英文摘要：
In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li, Shi, J. Math. Anal. Appl. 246, 308-319 (2000), clarify the assumptions and conclusions of their Theorem 1 as well as Theorem 2.5.2 in Borwein, Zhu, Techniques of Variational Analysis, Springer (2005) and streamline the proofs. Our main result, Theorem 3 is formulated in the metric space setting. When reduced to Banach spaces (Corollary 9), it extends and strengthens the smooth variational principle established in Borwein, Preiss, Trans. Amer. Math. Soc. 303, 517-527 (1987) along several directions.
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