Ekeland's variational principle for an (L)over-bar0-valued function on a complete random metric space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Guo, Tiexin¹ 

[1] Beihang Univ, LMIB, Beijing 100191, Peoples R China

关键词: Random metric space;    Random normed module;    (L)over-bar(0)-valued function;    Lower semicontinuity;    Ekeland's variational principle;    Bishop-Phelps theorem;   

DOI  :  10.1016/j.jmaa.2011.11.025

来源: Elsevier

【 摘 要 】

Motivated by the recent work on conditional risk measures, this paper studies the Ekeland's variational principle for a proper, lower semicontinuous and lower bounded (L)overbar(0)-valued function, where (L)overbar(0) is the set of equivalence classes of extended real-valued random variables on a probability space. First, we prove a general form of Ekeland's variational principle for such a function defined on a complete random metric space. Then, we give a more precise form of Ekeland's variational principle for such a local function on a complete random normed module. Finally, as applications, we establish the Bishop-Phelps theorem in a complete random normed module under the framework of random conjugate spaces. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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