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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]

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]

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]

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]

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 - 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]

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.