SOME PROPERTIES OF THE SET OF ALL STRONG UNIFORM CLUSTER POINTS

Abstract

The aim of this paper is to establish some relationship between the set of strong uniform statistical cluster points and the set of strong statistical cluster points of a given sequence in the probabilistic normed space. To this aim, let the uniform density be on the positive integers N for a sequence in the probabilistic normed space, that is, cases as equal of the lower and upper uniform density of a subset of N. We introduce the concept of strong uniform statistical cluster points and give a new type convergence in the probabilistic normed space. Note that the set of strong uniform statistical cluster points is a non-empty compact set. We also investigate some properties of the set all strong uniform cluster points of a sequence in the probabilistic normed space.