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The notion of relative uniform convergence of a sequence of functions was introduced and investigated by Moore, followed by E. W. Chittenden in the twentieth century. The concept attracted the researcher at the beginning, of the twenty-first century. Jackson F. H. initiated the concept of the notion of the quantum difference operator. We introduced the quantum difference sequence space m(ɸ, ru,∇p), p ≥ 0 of W.L.C. Sargent type. We examine its various properties such as solidity, convergence-free, completeness, etc. Also, some induction results have been established. [ABSTRACT FROM AUTHOR]

The Orlicz function-defined sequence spaces of functions by relative uniform convergence of sequences related to p -absolutely summable spaces are a new concept that is introduced in this article. We look at its various attributes, such as solidity, completeness, and symmetry. We also look at a few insertional connections involving these spaces. [ABSTRACT FROM AUTHOR]

The concept of statistical convergence plays a very prominent role in the study of sequence spaces. In this treatise, we extend the research on different types of statistical convergence viz., statistical convergence in mean, in measure, in distribution, in almost surely and with respect to uniformly almost surely of complex uncertain triple sequences in a given uncertainty space. We emphasize to focus on characterizing statistical convergence of complex uncertain triple sequence in some extent. Moreover, we initiate the notion of complex uncertain Cauchy triple sequence and establish the interconnection of it with a statistically convergent triple sequence. [ABSTRACT FROM AUTHOR]

In this article, we introduce the notion of relative uniform convergence, relative uniform Cauchy of difference sequence of functions and study the relation between these two notions. We define the sequence spaces l∞(Δ, ru); c(Δ, ru); c0(Δ, ru) and study their topological properties. [ABSTRACT FROM AUTHOR]

In this paper we introduce new sequence spaces with the help of domain of matrix D(r, 0, s, 0, t), and study some of their topological properties. Further, we determine β and γ duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings. [ABSTRACT FROM AUTHOR]

Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topo-logical properties of the defined sequence spaces along with the inclusion relations have been investigated. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the complex uncertain sequence space m (ϕ , Γ) related to the ℓ p (Γ) space. We have introduced the space m (ϕ , Γ) of almost surely, in measure, in mean, in distribution and uniformly almost surely. Also we have studied their different properties. [ABSTRACT FROM AUTHOR]

In this paper, we define almost convergence concepts of complex uncertain sequences: almost sure convergent, almost convergent in measure, almost convergent in mean and almost convergent in distribution and relationship among them are discussed. We also define Cesaro summable for complex uncertain sequence space. In addition, we derive relationships between convergent, Cesaro summable and almost convergent. [ABSTRACT FROM AUTHOR]

In this paper we introduce the sequence spaces c0i(Δ) ,ci(Δ) and li ∞ (Δ) of interval numbers and study some of their algebraic and topological properties. Also we investigate some inclusion relations related to these spaces. [ABSTRACT FROM AUTHOR]

Fine spectra of various matrices have been examined by several authors. In this article we have determined the fine spectrum of the upper triangular matrix U (r, 0, 0, s) on the sequence spaces c0 and c. [ABSTRACT FROM AUTHOR]

Fine spectra of various matrix operators on different sequence spaces have been examined by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the lower triangular matrix B (r, s,t) on the sequence space cs. In a further development, we have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator B (r, s,t) on the sequence space cs. [ABSTRACT FROM AUTHOR]

In this paper, we study the spectrum of the operator D(r, 0, 0, s) on a sequence space bv0, the space of all sequences x such that limn→∞ xn = 0 and ∥ x ∥ = Σ n=0∞ ∣ x n+1 - xn ∣ < ∞. [ABSTRACT FROM AUTHOR]

In this paper, we study the spectrum of the operator D(r, 0, 0, s) on a sequence space bv0, the space of all sequences x such that limn→∞ xn = 0 and ∥ x ∥ = Σ n=0∞ ∣ x n+1 - xn ∣ < ∞. [ABSTRACT FROM AUTHOR]

In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved. [ABSTRACT FROM AUTHOR]

In this paper we introduce the new classes of sequences $\ell _\infty ^F$ (M, A, &varphi;, p, Δr), mF(M, A, &varphi;, p, Δr) and CF(M, A, p, Δr) of fuzzy numbers defined by Orlicz function. We study their different properties and established some inclusion relation involving these classes of sequences. [ABSTRACT FROM AUTHOR]

The sequence spaces cF (M), cOF (M) and lF (M) of fuzzy real numbers with fuzzy metric are introduced. Some properties of these sequence spaces like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving these sequence spaces. [ABSTRACT FROM AUTHOR]

The sequence space re(M, Φ)F of fuzzy real numbers is introduced. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space. [ABSTRACT FROM AUTHOR]

In this paper we have examined the spectra of the operator D(r, 0, 0, s) on sequence spaces c0 and c. [ABSTRACT FROM AUTHOR]

We introduce the classes of generalized difference bounded, convergent, and null sequences of fuzzy real numbers defined by an Orlicz function. Some properties of these sequence spaces like solidness, symmetricity, and convergence-free are studied. We obtain some inclusion relations involving these sequence spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we have introduced the notion of fuzzy real-valued bounded variation double sequence space . We have studied some of its properties like convergence free, solidness, symmetricity, monotonicity, etc. We have proved some inclusion results too. [Copyright &y& Elsevier]

In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces $$ _2 \bar \ell _\infty (\Delta ,q), _2^ - c(\Delta ,q), _2^ - c^B (\Delta ,q), _2^ - c^R (\Delta ,q), _2^ - c^{BR} (\Delta ,q) $$ etc. being symmetric, solid, monotone, etc. We prove some inclusion results too. [ABSTRACT FROM AUTHOR]

In this paper we define the space |Np|(M,r,q,s) on seminormed complex linear space by using an Orlicz function and we study various properties and obtain some inclusion relations involving this space. This study generalizes some results of Bhardwaj and Singh [Demonstratio Math. 32 (1999) 539; Indian J. Pure Appl. Math. 31 (2000) 319]. [Copyright &y& Elsevier]