The Method of almost convergence with operator of the form fractional order and applications

The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those concepts are presented. Second, we construct the almost convergent spaces with fractional order difference operator and compute dual spaces which are help us in the characterization of matrix mappings. After we characterize to the matrix transformations, we give some examples.Comment: 20 pages, 4 table

ON LACUNARY CONVERGENCE IN CREDIBILITY SPACE

In this paper, we present the notions of lacunary statistically convergent sequence for fuzzy variables, lacunary statistically Cauchy sequence in credibility space, and present a kind of lacunary statistical completeness for credibility space. Also, we present lacunary strong convergence concepts of sequences of fuzzy variables of different types

THE EFFECT OF TECHNOLOGY IN DEVELOPING LISTENINGCOMPREHENSION SKILLS

In this article, the sequence spaces f0(Nt) and f (Nt) are introduced as the domain of Nörlund mean in the spaces f0 and f of almost null and almost convergent sequences which are isomorphic to the spaces f0 and f, respectively, and some inclusion relations are given. Additionally, alpha, beta and gamma duals of the sequence spaces f0(Nt) and f (Nt) are determined. Finally, the classes (λ(Nt): μ) and (μ: λ(Nt)) of matrix transformations are characterized for given sequence spaces λ and μ together with two Steinhaus type results

Almost and Strongly Almost B(er,se,et,ue)−Summable Double Sequences

In this paper, we define some new almost and strongly almost convergent double sequence spaces Be(Cf), Be(Cf0 ), Be[Cf ] and Be[Cf0 ] derived by the domain of four-dimensional sequential band matrix B(er,se,et,ue) in the spaces Cf , Cf0 , [Cf ] and [Cf0 ], respectively. Then we study some topological properties and prove some strict inclusion relations. Moreover, we calculate the α−,βbp− and γ−duals of the new spaces. Finally, we state some known lemmas concerning the four-dimensional matrix classes of almost convergent double sequences, then we characterize some new four-dimensional matrix transformations from and into the new sequence spaces Be(Cf) and Be[Cf ]. We conclude the paper with several significant results

Almost convergence and generalized difference matrix

Let f denotes the space of almost convergent sequences introduced by Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190] and (f) over cap also be the domain of the generalized difference matrix B(r, s) in the sequence space f. In this paper, the beta- and gamma-duals of the spaces f, fs and (f) over cap are determined. Furthermore, two basic results on the space f are proved and the classes ((f) over cap: mu) and (mu: (f) over cap) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where mu is any given sequence space. (C) 2010 Elsevier Ltd. All rights reserved