Some new difference sequence spaces

Aydın, Cafer; Başar, Feyzı

doi:10.1016/j.amc.2003.08.055

Cited by 80 publications

(60 citation statements)

References 3 publications

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“…So, the results related to the domain of the matrix B(r; s) are more general and more comprehensive than the consequences of the domain of the matrix , and include them. Now, following Sönmez and Başar [46] which is the continuation of Başar and Altay [15], and Ayd¬n and Başar [11], we proceed essentially di¤erent than K¬zmaz [24] and the other authors following him, and employ a technique of obtaining a new sequence space by means of the matrix domain of a triangle matrix.…”

Section: 2mentioning

confidence: 99%

“…If A is triangle, then one can easily observe that the sequence spaces X A and X are linearly isomorphic, i.e., X A = X. The idea constructing a new sequence space by means of the domain of a triangle matrix was employed by Wang [48], Ng and Lee [43], Malkowsky [29], Altay and Başar [1,2,3,4,5,6,7,8], Malkowsky and Savaş [33], Başar¬r [17,18], Başar¬r and Kay¬kç¬ [19], Başar¬r and Öztürk [20], Kara and Başar¬r [21], Kara et al [22], Ayd¬n and Başar [9,10,11,12,13], Başar et al [16],Şengönül and Başar [47], Altay [1], Polat and Başar [44] and, Malkowsky et al [30]. Additionally, c 0 (u; p) and c(u; p) are the spaces consisting of the sequences x = (x k ) such that ux = (u k x k ) is in the spaces c 0 (p) and c(p) for u 2 U, the set of sequences with non-zero entries, respectively, and studied by Başar¬r [17].…”

Section: Introductionmentioning

confidence: 99%

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Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces

Başar¹

2013

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces

Başar¹

2013

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…Some new sequence spaces 653 Then, there is some no € Ν by (6.5) We conclude the work by expressing from now on that the aim of the next paper is to study the difference sequence space α£(Δ) in the sense of Aydin and Ba §ar [6].…”

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confidence: 99%

SOME NEW SEQUENCE SPACES WHICH INCLUDE THE SPACES lP AND l∞

Aydm¹,

Başar²

2005

Demonstratio Mathematica

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Abstract. In the present paper, we introduce the sequence space a£ of non-absolute type and prove that the spaces a r v and lv are linearly isomorphic for 0 < ρ < oo. We also show that dp, which includes the space lp, is a p-normed space and a Β Κ space in the cases of 0 < ρ < 1 and 1 < ρ < oo, respectively. Furthermore, we give some inclusion relations and determine the α-, β-and 7-duals of the space a£ and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space a T v to some of the known sequence spaces and to some new sequence spaces. IntroductionBy w, we denote the space of all real or complex valued sequences. Any vector subspace of w is called as a sequence space. We write £oo, c and co for the spaces of all bounded, convergent and null sequences, respectively. Also by 6s, cs, £\ and £p, we denote the spaces of all bounded, convergent, absolutely and p-absolutely convergent series, respectively; whereA sequence space λ with a linear topology is called a K-space provided each of the maps p¿ : λ -> C defined by Pi(x) = Xi is continuous for all i 6 Ν; where C denotes the complex field and Ν = {0, 1, 2,...}. A Kspace Λ is called an FK-space provided λ is a complete linear metric space. An FK-space whose topology is normable is called a BK-space (see [9, pp. 272-273]).Let A = (anjt) be an infinite matrix of real or complex numbers αη*; where n, k € N. For the arbitrary sequence spaces λ and μ, the matrix A defines a mapping from λ into μ if for every sequence χ = (χ*) € λ the sequence Ax = {(ylx)n}) the ^4-transform of x, exists and is in μ; where {Ax)n = a nk^k-For simplicity in notation, here and in what follows, 1991 Mathematics Subject Classification: 46A45, 46B45, 46A35. Key words and phrases: sequence spaces of non-absolute type, Schauder basis, the α-, β-and 7-duals, matrix mappings.

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“…[4] have generalized difference sequence spaces. Aydın and Başar [5] have introduced some new difference sequence spaces. Also the notion of difference sequence has been extended by Mursaleen [6], Mursaleen and Noman [7], Malkowsky et al [8], and Bektaş et al [9].…”

Section: Introductionmentioning

confidence: 99%

Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

Kadak

2015

International Journal of Mathematics and Mathematical Sciences

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We generalize the lacunary statistical convergence by introducing the generalized difference operator Δ ] of fractional order, where is a proper fraction and ] = (] ) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.

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Some new difference sequence spaces

Cited by 80 publications

References 3 publications

Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces

Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces

SOME NEW SEQUENCE SPACES WHICH INCLUDE THE SPACES lP AND l∞

Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

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