The Bishop-Phelps theorem in complete random normed modules endowed with the (ε, λ)-topology

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:391

Article

Wu, Mingzhi

关键词: Random normed module;    (epsilon, lambda)-topology;    Closed L-0-convex set;    Bishop-Phelps theorem;   

DOI  :  10.1016/j.jmaa.2012.02.037

来源: Elsevier

【 摘 要 】

In this paper, we adopt a new approach so that we can prove that the Bishop-Phelps theorem in complete random normed modules still holds under the (epsilon, lambda)-topology, which solves an open problem posed in [T.X. Guo, Y.J. Yang, Ekeland's variational principle for an L-0-valued function on a complete random metric space, J. Math. Anal. Appl. 389 (2012) 1-14]. (C) 2012 Elsevier Inc. All rights reserved

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