Ideal Convergent Sequences Research Articles

Continuous Projections onto Ideal Convergent Sequences

Let $\mathcal{I}\subseteq\mathcal{P}(\omega)$ be a meager ideal. Then there are no continuous projections from $\ell_\infty$ onto the set of bounded sequences which are $\mathcal{I}$-convergent to $0$. In particular, it follows that the set of bounded sequences statistically convergent to $0$ is not isomorphic to $\ell_\infty$.

Some new classes of paranorm ideal convergent double sequences of sigma-bounded variation over n-normed spaces

The sequence space , the space of all sequence of -bounded variation, was firstly defined and studied by Mursaleen. Later on, Vakeel and Tabassum developed the same space to double sequences. Recen...

On Some New Ideal Convergent Sequence Spaces of -Method of Summability

Bu calismada Norlund metodunun bir genellesmesi olarak P.N. Natarajan [On the -method of summability, Analysis] tarafindan tanimlanan -toplanabilme metodu kullanilarak bazi ideal yakinsak dizi uzaylari tanimlanmistir. Ayrica, bu uzaylarin bazi topolojik ozellikleri incelenmistir.

Some New Spaces of Ideal Convergent Double Sequences by Using Compact Operator

Some New Spaces of Ideal Convergent Double Sequences by Using Compact Operator

On Zweier generalized difference ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

Let $\mathbf{M}=(M_k)$ be a Musielak-Orlicz function. In this article, we introduce a new class of ideal convergent sequence spaces defined by Musielak-Orlicz function, using an infinite matrix, and a generalized difference matrix operator $B_{(i)}^{p}$ in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We obtainsome relations related to these sequence spaces.

Some classes of ideal convergent sequences and generalized difference matrix operator

An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $u=(u_k)$ of real numbers is said to be $B^{n}_{(m)}$-ideal convergent to a real number $\ell$ for every $\varepsilon>0,$ the set $$\left\{k\in\mathbb{N}: |B^{n}_{(m)} u_k - \ell|\geq \varepsilon\right\}$$ belongs to $I,$ where $n,m\in\mathbb{N}.$ In this article we introduce the classes of ideal convergent sequences using a new generalized difference matrix $B^{n}_{(m)}$ and Orlicz functions and study their basic facts. Also we investigate the different algebraic and topological properties of these classes of sequences.

On some Generalized Nörlund Ideal Convergent Sequence Spaces

In this paper, some new Ideal convergent sequence spaces 14cN,p,qI , (c0)N,p,qI> and 14(l∞)N,p,qI> that are related to the 14(N,p,q)-> summability method, are introduced and some topological properties of these spaces and some inclusion relations and results are determined.

Ideally slowly oscillating sequences

An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the notion of ideally slowly oscillating sequences, which is lying between ideal convergent and ideal quasi-Cauchy sequences, and study on ideally slowly oscillating continuous functions, and ideally slowly oscillating compactness.

On some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operator

In this article we introduce multiplier type ideal convergent sequence spaces using Zweier transform and de la Vallee Poussin mean. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces.

Lacunary ideal convergence of multiple sequences

An ideal I is a family of subsets of N×N which is closed under taking finite unions and subsets of its elements. In this article, the concept of lacunary ideal convergence of double sequences has been introduced. Also the relation between lacunary ideal convergent and lacunary Cauchy double sequences has been established. Furthermore, the notions of lacunary ideal limit point and lacunary ideal cluster points have been introduced and find the relation between these two notions. Finally, we have studied the properties such as solidity, monotonic.

On σ-bounded variation and ideal convergence of fuzzy sequences

An ideal I is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper we introduce ideal convergent sequence spaces of fuzzy numbers using σ-bounded variation and Orlicz functions and study some basic topological and algebraic properties of these spaces. Finally we investigate the inclusions relations related to these spaces.

STRONGLY ALMOST IDEAL CONVERGENT SEQUENCES IN A LOCALLY CONVEX SPACE DEFINED BY MUSIELAK-ORLICZ FUNCTION

In this article, we introduce a new class of ideal convergent sequence spaces using an innite matrix, Musielak-Orlicz function and a new generalized dierence matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

Zweier Ideal Convergent Sequence Spaces Defined By Orlicz Functions

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this article we introduce ideal convergent sequence spaces using Zweier transform and Orlicz function. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces.

Lacunary ideal convergent double sequences of fuzzy real numbers

Lacunary ideal convergent double sequences of fuzzy real numbers

On σ-uniform density and ideal convergent sequences of fuzzy real numbers

An ideal I is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper we have introduced ideal convergent sequences of fuzzy real numbers using σ-uniform density. Furthermore, inclusion between Iσ-convergence and invariant convergence also Iσ-convergence and $[V_{\sigma}]^{F}_p$-convergence were given.

Some Ideal Convergent Sequence Spaces Defined by a Sequence of Modulus Functions Over n-Normed Spaces

In the present paper we study some ideal convergent sequence spaces defined by a sequence of modulus functions in n-normed spaces and examine some topological properties and inclusion relations between these spaces. Keywords: Lacunary sequence; Difference sequence space; Modulus function; Ideal convergence; n-normed space. 2010 Mathematics Subject Classification: 40A05; 40C05; 46A45

On paranormed Zweier ideal convergent sequence spaces defined By Orlicz function

In this article we introduce paranorm ideal convergent sequence spaces using Zweier transform and Orlicz function. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces.

On ideal convergent sequences in fuzzy normed linear spaces

In this article we introduce the notion of \(I\)-convergent and \(I\)-Cauchy sequence in a fuzzy normed linear space and establish some basic results related to these notions. Further, we define \(I\)-limit points and \(I\)-cluster points of a sequence in a fuzzy normed linear space and investigate the relations between these concepts.

Lacunary difference ideal convergent sequence spaces of fuzzy numbers

In this article, using the Orlicz function M and the difference operator of order n ≥ 1, we introduce the spaces of lacunary ideal convergent difference sequences and lacunary strongly summable difference sequences of fuzzy numbers via fuzzy metric. We also established some relations related to these spaces. Further, we study some basic topological properties of these spaces.

On generalized A- difference strongly summable sequence spaces defined by ideal convergence on a real n-normed space

In this article, we shall introduce a new class of ideal convergent (briefly I-convergent) sequence spaces using, infinite matrix, an Orlicz function and difference operator defined on n-normed spaces. We study these spaces for some linear topological structures and algebraic properties. We also give some relations related to these sequence spaces.Mathematics Subject Classification 2010: 40A05; 40B50; 46A19; 46A45.