Fuzzifying bornological linear spaces

In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided.

On the Uniqueness of p-Best Approximation in Probabilistic Normed Spaces

The main aim of this paper is to present some basic as well as essential results involving the notion of p-Chebyshev sets in probabilistic normed spaces. In particular, we discuss the convexity of p-Chebyshev sets, decomposition of the space into its special subspaces, and we see a characterization of p-Chebyshev sets in quotient spaces.