Abstract
We studied the best approximation between two sets in probabilistic normed spaces. We defined the best approximation on these spaces and generalized some definitions such as set of best approximation, p-proximinal set and p-approximately compact relative to any set and proved some theorems about them.
Highlights
An interesting and important generalization of the notion of metric space was introduced by Menger[1] under the name of statistical metric space, which is called probabilistic metric space
We introduce the concept of best approximation in probabilistic normed spaces and present some results
Definition 2.3: For a probabilistic normed space X and nonempty subsets A and C a sequence an∈A is said to converge in distance to C if ( ) ( ) limn→∞ υan −C t = υA−C t
Summary
An interesting and important generalization of the notion of metric space was introduced by Menger[1] under the name of statistical metric space, which is called probabilistic metric space. Definition 2.1: Let A and C are two nonempty subset of a probabilistic normed space (V, υ, τ). Definition 2.3: For a probabilistic normed space X and nonempty subsets A and C a sequence an∈A is said to converge in distance to C if ( ) ( ) limn→∞ υan −C t = υA−C t .
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