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In the present paper, we introduce and study the strong Cesaro summability of difference sequence spaces through fusion of modulus function. On the newly established sequence space, linear structure is imposed and a paranorm is established. Apart from various inclusion relations, a new variant of statistical convergence is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we define and discuss the Orlicz sequence spaces ΓM(∆n u, q, s) and ΓM(p, ∆n u, q, s) of entire sequences, where (X, q) is a seminormed space and s is any real number such that s ≥ 0. Furthermore, we study some topological properties of these spaces. We discuss some inclusion relations between them and related results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the difference sequence space ces(Bμ ∧, F, q) using sequence of modulus function F = (fi). We examine some topological properties of the space and also obtain some inclusion relations. [ABSTRACT FROM AUTHOR]

Let Δ − n be the backward difference operator of order −n. In this paper, we study some properties of the matrix domain associated with this operator and after computing α-, β-, γ-duals, we characterize some matrix classes on this space. Moreover, we investigate the problem of finding the norm of well-known operators such as Cesàro and Hilbert from ℓ p (Δ − n) into ℓ p. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the problem of finding the norm of Hilbert operator on some sequence spaces. Meanwhile, we obtain several interesting inequalities and inclusions. [ABSTRACT FROM AUTHOR]

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and l∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces. [ABSTRACT FROM AUTHOR]

The main purpose of the paper is to generalize the notions of the Köthe-Toeplitz duals and Null duals of sequence spaces by introducing the concepts of αEF-, βEF-, γEF-duals and NEF-duals, where E = ( E ) and F = ( F ) are two partitions of finite subsets of the positive integers. These duals are computed for the classical sequence spaces l and c . The other purpose of the paper is to introduce the sequence spaces . where $$X \in \left\{ {{l_\infty },\;c,\;{c_0}} \right\}$$ . We investigate the topological properties of these spaces, establish some inclusion relations between them, and compute the NEF-(or Null) duals for these spaces. [ABSTRACT FROM AUTHOR]

In this paper, we define the space Sαθ (Δmv, f) of all (Δmv, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator Δmv and real number α ∈ (0, 1]. We also introduce the space ωαθ (Δmv, f) of all strong (Δmv, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sαθ (Δmv, f) and ωαθ (Δmv, f) are established undercertain conditions. [ABSTRACT FROM AUTHOR]

Let be a non-negative matrix and be the forward difference operator of order n for . Denote by the infimum of those U, satisfying the following inequality: where and . This paper is focused on the problem of finding , where A is a matrix operator from into . In particular, we apply our results to well known matrix operators such as Copson, Hilbert, and Nörlund. [ABSTRACT FROM AUTHOR]

In this paper we define certain difference sequence spaces via n-normed space and a sequence of Orlicz function without convexity. We also make an effort to investigate their structural and some topological properties. Finally, we broaden this idea to double sequences and establish a new matrix theoretic approach for construction of double sequence spaces over n-normed spaces. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study triple difference sequence spaces over n-normed space via the sequence of modulus functions. Some algebraic and topological properties of the newly constructed spaces are also established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ2 sequence spaces over p-metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform Δ2 condition, and we also discuss some topological properties of the resulting spaces of χ2 with respect to ideal structures which is solid and monotone. Hence, given an example of the space χ2, this is not solid and not monotone. This theory is very useful for statistical convergence and also is applicable to rough convergence. [ABSTRACT FROM AUTHOR]

Abstract Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F̂ and ideal convergence defined the notion of c0I(Fˆ) $c_{0}^{I}(\hat{F})$, cI(Fˆ) $c^{I}(\hat{F})$ and l∞I(Fˆ) $l_{\infty }^{I}(\hat{F})$. In this paper, we give the ideal convergence of Fibonacci difference sequence space in intuitionistic fuzzy normed space with respect to fuzzy norm (μ,ν) $(\mu ,\nu )$. Moreover, we investigate some basic properties of the said spaces such as linearity, hausdorffness.

In this paper we define certain generalized double difference sequence spaces by means of an Orlicz function in 2-normed spaces. We prove that these spaces are Banach spaces and establish some inclusion relations. We also determine the α- and β(t)-dual of spaces M u(M, Δn,u, w, ǁ., .ǁ) and Ct(M, Δ n, u, w, ǁ., .ǁ), respectively. Finally, we characterize the classes (μ :Cϑ(M,Δn,u,w, ǁ.,.ǁ)) for ϑ∊{p,bp,t} of matrix transformations where p is any given space of double sequences. [ABSTRACT FROM AUTHOR]

The object of this paper is to introduce a new class of ideal convergent (briefly I-convergent) sequence spaces using an infinite matrix, sequence of modulus functions and difference operator defined on n-normed spaces. We study these spaces for some linear topological structures and algebraic properties. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we define the Lucas difference sequence spaces by the help of Lucas sequence and a sequence of modulus function. Besides, we give some inclusion relations and examine geometrical properties such as Banach-Saks type p, weak fixed point property. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of λmnk - χ3 and Λ3 sequences. Further, we introduce the spaces . . . and . . . which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces χ3 and Λ3, respectively. Moreover, we establish some inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of λmnk - Γ³ and Λ³ sequences. Further, we introduce the spaces ... and ..., which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces Γ³ and Λ³, respectively. Moreover, we establish some inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of λmnk - Γ³ and Λ³ sequences. Further, we introduce the spaces ... and ..., which are of nonabsolute type and we prove that these spaces are linearly isomorphic to the spaces Γ3 and Λ3; respectively. Moreover, we establish some inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach for construction of such double sequence spaces. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study deferred Cesrào statistical convergence of order (ξ, ω) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for ξ ≤ ω and convergence is not possible for ξ > ω. We also define p-deferred Cesàro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesàro statistical convergent of order (ξ, ω) in (Δ, F, f), then it need not be strongly p-deferred Cesàro summable of order (ξ, ω) in general for 0 < ξ ≤ ω ≤ 1. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we focus on the problem of finding the norm of Hilbert operator on some sequence spaces. Meanwhile, we obtain several interesting inequalities and inclusions.

In this research, we investigate two types of Copson matrices, the generalized Copson matrix and the Copson matrix of order n, and their associated sequence spaces generated by these matrices. We also investigate the topological properties, inclusions, and dual spaces of these new Banach spaces as well as compute the norm of Copson operators on the well-known matrix domains such as Hilbert and difference sequence spaces. Moreover, in a reverse manner, we investigate the norm of well-known operators on the Copson matrix domains generated with Copson matrices. Through this study we introduce several new inequalities, inclusions, and factorizations for well-known operators. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of $\lambda_{mn}-\chi^{2}$ and $\Lambda^{2}$ sequences. Further, we introduce the spaces $\left[\chi^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)}$ and $\left[\Lambda^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)},$ which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces $\chi^{2}$ and $\Lambda^{2},$ respectively. Moreover, we establish some inclusion relations between these spaces.

In this paper we construct some difference new modular sequence spaces defined by a sequence of Orlicz functions over n-normed spaces. We also study several properties relevant to topological structures and interrelationship between these spaces.

In this paper, we define the sequence spaces: $\chi^{2qu}_{f\mu}\left(\Delta\right)$ and $\Lambda^{2qu}_{f\mu}\left(\Delta\right),$ where for any sequence $x=\left(x_{mn}\right),$ the difference sequence $\Delta x$ is given by $\left(\Delta x_{mn}\right)_{m,n=1}^{\infty}=\left[\left(x_{mn}-x_{mn+1}\right)-\left(x_{m+1n}-x_{m+1n+1}\right)\right]_{m,n=1}^{\infty}.$ We also study some properties and theorems of these spaces.

In this paper we introduce the I- of χ2 sequence spaces over p-metric spaces defined by Musielak function. We also examine some topological properties and prove some inclusion relation between these spaces.

In this article we introduce the sequence spaces [χ2qfμ,||(d(x1,0),d(x2,0),...,d(xn-1),0))||p]χI(F) and [Λ2qfμ,||(d(x1,0),d(x2,0),...,d(xn-1),0))||p]χI(F) associated with the integrated sequence space defined by Musielak. We study some basic topological and algebraic properties of these spaces. We also investigate some inclusion relations related to these spaces. [ABSTRACT FROM AUTHOR]