Ideal Convergence and Completeness of a Normed Space

Lacunary Ideal Convergence in Probabilistic Normed Space

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

A-Sequence Spaces in 2-Normed Space Defined by Ideal Convergence and an Orlicz Function

and Applied Analysis 3 of positive real numbers. By S 2 − X , we denote the space of all sequences defined over X, ‖·, ·‖ . Now we define the following sequence spaces: W ( M,Δ, p, ‖, ·, ‖ ⎧ ⎪⎨ ⎪⎩ x ∈ S 2 −X : ∀ε > 0 { n ∈ : ∞ ∑ k 1 ank [ M (∥ ∥ ∥ ∥ Δxk − L ρ , z ∥ ∥ ∥ ∥ )]pk ≥ ε } ∈ I for some ρ > 0, L ∈ X and each z ∈ X ⎫ ⎪⎬ ⎪⎭ , W 0 ( A,M,Δ, p, ‖, ·, ‖ ⎧ ⎪⎨ ⎪⎩ x ∈ S 2 −X : ∀ε > 0 { n ∈ : ∞ ∑...

Fuzzy normed space of operators and its completeness

In this thesis, In this thesis, general structure of fuzzy normed linear spaces is examined and basic concepts of bounded and continuous operators defined on these spaces are studied. Firstly, fuzzy norm on finite-dimensional linear spaces is defined and by means of α -cut set some properties of this norm are mentioned. In the second part, generalizing the definition of fuzzy norm given on fini...

On Ideal Convergence of Double Sequences in Probabilistic Normed Spaces

One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al. [12]. In this paper, we define and study the concept of I-convergence, I∗-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I ∗ 2 -convergence, i.e., we show that I ∗ 2 -convergence...

Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces