On Hilbert I-convergent sequence spaces

2013

In this article we introduce the sequence spaces V I 0σ(m, ) and V I σ (m, ) and study some of the properties and inclusion relations on these spaces. Mathematics Subject Classification: 40A05, 40A35, 40C05, 46A45

Journal of Mathematics and Computer Science

In this paper, we use the notion of ideal convergence (I-convergence) to introduce Tribonacci I-convergent sequence spaces, that is, c I 0 (T), c I (T) and l I ∞ (T) as a domain of regular Tribonacci matrix T = (t jn) (constructed by the Tribonacci sequence). We also present few inclusion relations and prove some topological and algebraic properties based results with respect to these spaces.

Numerical Functional Analysis and Optimization, 2018

The notation of I-convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I-convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces.

Analysis, 2012

The sequence space BV was introduced and studied by Mursaleen [10]. In this article we introduce the sequence space BV I and study some of the properties of this space.

ZANCO JOURNAL OF PURE AND APPLIED SCIENCES, 2016

2016

In this work, we introduce some new generalized sequence space related to the space ℓ(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute α-, β-and γ-duals of this space, and characterize certain matrix transformations on this sequence space. In studying the sequence spaces, especially, to obtain new sequence spaces, in general, the matrix domain µ A of an infinite matrix A defined by µ A = {x = (x k ) ∈ w : Ax ∈ µ} is used. In the most cases, the new sequence space µ A generated by a sequence space µ is the expansion or the contraction of the original space µ. In some cases, these spaces could be overlap. Indeed, one can easily see that the inclusion µ S ⊂ µ strictly holds for µ ∈ {ℓ ∞ , c, c 0 }. Similarly one can deduce that the inclusion µ ⊂ µ ∆ also strictly holds for µ ∈ {ℓ ∞ , c, c 0 }; where S and ∆ are matrix operators. Recently, in [14], Mursaleen and Noman constructed new sequence spaces by using matrix domain over a normed space. They also studied some topological properties and inclusion relations of these spaces. It is well known that paranormed spaces have more general properties than the normed spaces. In this work, we generalize the normed sequence spaces defined by Mursaleen [14] to the paranormed spaces. Furthermore we introduce new sequence space over the paranormed space. Next we investigate behaviors of this sequence space according to topological properties and inclusion relations. Finally we give certain matrix transformation on this sequence space and its duals. In the literature, by using the matrix domain over the paranormed spaces, many authors have defined new sequence spaces. Some of them are as the following. For example; Choudhary and Mishra [6] have defined the sequence space ℓ(p) which the S-transform is in ℓ (p), Basar and Altay([4],[5]) defined the spaces λ (u, v; p) = {λ (p)} G for λ ∈ {ℓ ∞ , c, c 0 } and ℓ (u, v; p) = {ℓ (p)} G respectively, and Altay and Basar [1] have defined the spaces r t ∞ (p) , r t c (p) , r t 0 (p). In [8], Karakaya and Polat defined and examined the spaces e r 0 (∆; p) , e r (∆; p) , e r ∞ (∆; p), and Karakaya, Noman and Polat [9] have recently introduced and studied the spaces ℓ ∞ (λ, p) , c (λ, p), c 0 (λ, p); where R t and E r denote the Riesz and the Euler means,

Communications in Mathematical Analysis, 2016

In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from $l_p$ into $ l_p(E,Delta)$, and apply our results to Copson and Hilbert matrices.

Applied Mathematics and Computation, 2004

The idea of difference sequence spaces was introduced by Kızmaz [Canad. Math. Bull. 24 (1981) 169] and this concept was generalized by Et and C ß olak [Soochow J. Math. 21 (1995) 337]. In this paper we define the sequence spaces ' 1 ðpÞðD r v Þ, cðpÞðD r v Þ, c 0 ðpÞðD r v Þ and cðpÞðD r v Þ, ðr 2 NÞ, give some topological properties and inclusion relations of these sequence spaces.

Acta Scientiarum. Technology

In this paper, by using the triangle Hilbert matrix and the notion of ideal convergence for the sequences in intuitionistic fuzzy normed spaces, we introduce some new intuitionistic fuzzy normed sequence spaces as a domain of Hilbert matrix , that is, ❑ 0(,) () and ❑ (,) () Here, ❑ 0(,) () denotes the Hilbert ideal null convergent sequence space with respect to the intuitionistic fuzzy norm and ❑ (,) () denotes the Hilbert ideal convergent sequence space with respect to the intuitionistic fuzzy norm We also define an open ball with respect to defined sequence space and prove that these open balls are the open sets of these spaces Further, we study some of its topological and algebraic properties We prove that these sequence spaces are linear spaces of In addition, we define a topology with respect to these sequence spaces and obtain that the defined topology is first countable and these topological sequence spaces are Hausdorff spaces We also obtain if and only if results that give an idea about when a sequence belonging to these spaces is classical convergent with respect to the intuitionistic fuzzy norm and when a sequence belonging to these spaces is ideal convergent with respect to the intuitionistic fuzzy norm