Best approximation on probabilistic normed spaces. (English) Zbl 1200.46072

Summary: The main purpose of this paper is to study the best approximation in probabilistic normed spaces. We define the best approximation in these spaces and generalize some definitions such as set of best approximation, proximinal set and approximatively compact set. Then we prove some theorems about them.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


46S50 Functional analysis in probabilistic metric linear spaces
41A50 Best approximation, Chebyshev systems
46B20 Geometry and structure of normed linear spaces
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