The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilis...

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

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

We define the (w∗-) boundedness property and the (w∗-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w∗-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of tw...

The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilis...

In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space a...