Double Sequence Spaces Research Articles

Norm inequalities involving upper bounds for certain matrix operators on Orlicz–Euler and Orlicz–Taylor double sequence spaces

Norm inequalities involving upper bounds for certain matrix operators on Orlicz–Euler and Orlicz–Taylor double sequence spaces

Double Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function

The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of research in social science, management science, and mathematics. In this paper, we use the concept of Fuzzy real numbers to introduce and study the new double sequence spaces l∞ (M, λ, ρ), C F (M, λ, ρ) and CoF (M, λ, ρ) of fuzzy real numbers defined by the Orlicz function and study some of their properties like linear space structure, completeness, and solidness.

Some Results Related to New Jordan Totient Double Sequence Spaces

The 4 dimensional (4d) Jordan totient matrix which is described by the aid of the famous Jordan's function and some new Jordan totient double sequence spaces described as the domain of this aforementioned matrix have been examined by Erdem and Demiriz . In the present paper, first of all we define two new double sequence spaces by using the 4d Jordan totient matrix and we show that this newly described double sequence spaces are Banach spaces with their norm. Then, we give some inclusion relations including this spaces. Moreover, we compute the $\alpha$-, $\beta(bp)$- and $\gamma$-duals and finally, we characterize some new 4d matrix transformation classes and complete this work with some significant results.

Solvability of infinite systems of fractional differential equations in the double sequence space $$ 2^c(\triangle )$$

In this work, we first introduce the concept of double sequence space $$2^c(\triangle )$$ . Then, we construct a Hausdorff measure of noncompactness on this space. Furthermore, by employing this measure of noncompactness we discuss the existence of solutions for infinite systems of third-order three-point boundary value problem in the double sequence space $$2^c(\triangle )$$ . Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result.

Upper bounds of some matrix operators on binomial and Orlicz-binomial double sequence spaces

In this article, we introduce binomial double sequence space bk(α,β;γ,δ)(1≤k≤∞) and Orlicz-binomial double sequence space bφ(α,β;γ,δ), and obtain certain inclusion results related to these spaces. We further focus on estimating the upper bounds for ∥M∥Lk,bk(α,β;γ,δ) and ∥M∥Lφ,bφ(α,β;γ,δ), where M is four dimensional Hausdorff matrix or four dimensional Nörlund matrix. We establish a Hardy type inequality in the case of four dimensional Hausdorff matrix.

On ℷ-Convergent For Double Sequence Spaces of Fuzzy Numbers Described by Double Orlicz Functions

On ℷ-Convergent For Double Sequence Spaces of Fuzzy Numbers Described by Double Orlicz Functions

A Study on Strongly Almost Convergent and Strongly Almost Null Binomial Double Sequence Spaces

The 4 dimensional (4d) binomial matrix and its domains on the classical double sequence spaces $\mathcal{L}_{p}$, $\mathcal{M}_{u}$, $\mathcal{C}_{P}$, $\mathcal{C}_{bP}$, $\mathcal{C}_{r}$, $\mathcal{C}_{f}$ and $\mathcal{C}_{f_0}$ have been described and examined by Demiriz and Erdem in the papers \cite{e.d.2}-\cite{e.d.3}. In this article, we describe two double sequence spaces with the aid of the aforementioned matrix and study some properties of these. After giving inclusion relations, we compute $\alpha-$, $\beta(bp)-$ and $\gamma-$duals and give some new matrix classes related them.

Integrability on the Abstract Wiener Space of Double Sequences and Fernique Theorem

The integrability of a function defined on the abstract Wiener space of double Fourier coefficients is explored. The abstract Wiener space is also a Hilbert space. We define an orthonormal system of the Hilbert space to establish a measure and integration on the abstract Wiener space. We examine the integrability of a function e α · 2 defined on the abstract Wiener space for Fernique theorem. With respect to the abstract Wiener measure, the integral of the function turns out to be convergent for α < 1 / 2 . The result provides a wider choice of the constant α than that of Fernique.

On the domain of difference double sequence spaces of arbitrary orders

Abstract The prime objective of this paper is to define a new double difference operator with arbitrary order via which new classes of difference double sequences are introduced. Results on topological structures, dual spaces and four-dimensional matrix mappings related to the proposed difference double sequence spaces are discussed. As an application of this work, the proposed operator is being used to approximate partial derivatives of fractional orders. Some numerical examples are also given in support of the validity or the clear visualization of the results obtained.

On Ideal Convergent Difference Double Sequence Spaces in Intuitionistic Fuzzy Normed Linear Spaces

In this paper, we introduce difference double sequence spaces ${I_{2} }^{(\mu,\upsilon)}(M,\Delta)$ and ${I_{2}^{0}}^{(\mu,\upsilon)}(M,\Delta)$ in the intuitionistic fuzzy normed linear spaces. We also investigate some topological properties of these spaces.

Some Double Sequence Spaces Generated by Four-Dimensional Pascal Matrix

The purpose of this paper is to discover and examine a four-dimensional Pascal matrix domain on Pascal sequence spaces. We show that they are spaces and also establish their Schauder basis, topological properties, isomorphism and some inclusions.

A New RH-Regular Matrix Derived by Jordan’s Function and Its Domains on Some Double Sequence Spaces

In the present study, we introduce a new RH-regular 4D (4-dimensional) matrix derived by Jordan’s function and define double sequence spaces by using domains of 4D Jordan totient matrixJton some classical double sequence spaces. Also, theα-,βϑ-, andγ-duals of these spaces are determined. Finally, some classes of 4D matrices on these spaces are characterized.

Cyclic behavior of holomorphic functions on a Runge region

Let Ω⊂CN be a Runge region and let H(Ω) denote the Fréchet space of holomorphic functions on Ω. In this paper, we provide extensions of some earlier results regarding nonscalar continuous linear operators on H(Ω) commuting with each partial differentiation operator ∂∂zk, where 1≤k≤N. Specifically, we demonstrate that all such operators are hypercyclic and share a dense set of common cyclic vectors. Motivated by our results, we introduce a class of finite sets of Fréchet space operators patterned after the partial differentiation operators, called backward multi-shifts, and show that any nonscalar operator in the commutant of such a finite set is supercyclic. Lastly, we apply our supercyclicity result on weighted differentiation operators on H(CN) and also on double sequence spaces.

The spaces of B(r,s,t,u) strongly almost convergent double sequences and matrix transformations

Most recently, some new double sequence spaces B(Mu), B(Cϑ) where ϑ={b,bp,r,f,f0} and B(Lq) for 0<q<∞ have been introduced as the domain of four-dimensional generalized difference matrix B(r,s,t,u) in the double sequence spaces Mu, Cϑ where ϑ={b,bp,r,f,f0} and Lq for 0<q<∞, and some topological properties, dual spaces, some new four-dimensional matrix classes and matrix transformations related to these spaces have also been studied by Tuğ and Başar and Tuğ (see [1–4]). In this paper, we introduce new strongly almost convergent double sequence spaces B[Cf] and B[Cf0] whose B(r,s,t,u)-transforms are in the spaces [Cf] and [Cf0], respectively. The main body of this paper is designed by the investigation of the following hypothesis. Firstly, we examine some topological properties and inclusion relations including the new double sequence spaces B[Cf] and B[Cf0]. Also, we determine the α-dual, β(bp)-dual and γ-dual of the space B[Cf]. Finally, we give the necessary and sufficient conditions on an infinite matrix transforming from [Cf] over Cf, and we also characterize the classes ([Cf];Mu), (B[Cf];Cf) and (B[Cf];Mu).

Difference Cesàro Double Sequence Space Defined by Double Orlicz Function

In this article, we are provide a suitable generalization of difference Cesàro double sequence spaces defined by double Orlicz functions and Study different topological properties and inclusion relationships using new kinds of double sequence spaces to generalize some known results of double Orlicz functions.

Some New Double Sequence Spaces of Fuzzy Numbers Defined by Double Orlicz Functions Using A Fuzzy Metric

This paper presents some new double sequence spaces using a double Orlicz functions and a fuzzy metric. Using the idea that a nonnegative, upper-semi continuous, normal and convex fuzzy number is the distance between two points in a fuzzy metric, we test some basic properties of the new double sequence spaces of fuzzy numbers. We also analyze the relationships between these spaces.

I - Convergence of Difference Double Sequence Space of Fuzzy Real Number Defined by Double Orlicz Function

In this paper, we introduced I - Convergence of Difference Double Sequence Space of Fuzzy Real Number Defined by Double Orlicz Function and study different topological properties of these sequence space like solidity, symmetricity, etc. We also obtain some inclusion relations involving these sequence spaces.

The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

On the New Double Binomial Sequence Space

The aim of this paper is to present the new double Binomial sequence space $\mathcal{B}_{p}^{r,s}$ which consists of all sequences whose double Binomial transforms of orders $r,s$ ($r$ and $s$ are nonzero real numbers with $r+s \neq 0$) are in the space $\mathcal{L}_p$, where $0&amp;lt;p&amp;lt;\infty$. We examine its topological and algebraic properties and inclusion relations. Furthermore, the $\alpha-$, $\beta(bp)-$ and $\gamma-$duals of the space $\mathcal{B}_{p}^{r,s}$ are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

4-Dimensional Euler-Totient Matrix Operator and Some Double Sequence Spaces

Our main purpose in this study is to define&#x0D; the 4-dimensional Euler-Totient matrix operator and to investigate the matrix domains&#x0D; of this matrix on the classical double sequence spaces $\mathcal{M}_{u}$, $\mathcal{C}_{p}$, $\mathcal{C}_{bp}$ and $\mathcal{C}_{r}$.&#x0D; Besides these, we examine their topological and algebraic properties and give inclusion relations about the new spaces.&#x0D; Also, the $\alpha-$, $\beta(\vartheta)-$ and $\gamma-$duals of these spaces are determined and finally, some matrix classes are characterized.