On the Paranormed Space of Bounded Variation Double Sequences

2019 ◽  
Vol 43 (3) ◽  
pp. 2701-2712
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Bounded Variation ◽  
Double Sequences ◽  
Paranormed Space

scholarly journals On the paranormed space L(t) of double sequences

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1043-1053 ◽  
Author(s):  
Hüsamettin Çapan ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Double Sequences ◽  
Paranormed Space ◽  
Dimensional Matrix ◽  
Paranormed Sequence Space ◽  
Alpha Beta

In this paper, we introduce the paranormed sequence space L(t) which is the generalization of the space Lq of all absolutely q-summable double sequences. We examine some topological properties of the space L(t) and determine its alpha-, beta- and gamma-duals. Finally, we characterize some classes of four-dimensional matrix transformations from the space L(t) into some spaces of double sequences.

scholarly journals On the paranormed space $\mathcal{M}_{u}(t)$ of double sequences

2017 ◽  
Vol 37 (3) ◽  
pp. 99-111 ◽  
Author(s):  
Feyzi Başar ◽  
Hüsamettin Çapan
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Double Sequences ◽  
Paranormed Space ◽  
Dual Spaces ◽  
Dimensional Matrix ◽  
Paranormed Sequence Space ◽  
Alpha Beta

In this paper, we introduce the paranormed sequence space $\mathcal{M}_{u}(t)$ corresponding to the normed space $\mathcal{M}_{u}$ of bounded double sequences. We examine general topological properties of this space and determine its alpha-, beta- and gamma-duals. Furthermore, we characterize some classes of four-dimensional matrix transformations concerning this space and its dual spaces.

scholarly journals A Note on the Definition of Bounded Variation of Higher Order for Double Sequences

2020 ◽  
Vol 44 (4) ◽  
pp. 563-570
Author(s):  
BHIKHA LILA GHODADRA ◽  
VANDA FÜLÖP
Keyword(s):  
Bounded Variation ◽  
Higher Order ◽  
Double Sequences ◽  
Inclusion Relations ◽  
Definition Of

In this study the definition of bounded variation of order p (p ∈ ℕ) for double sequences is considered. Some inclusion relations are proved and counter examples are provided for ensuring proper inclusions.

scholarly journals Some new classes of paranorm ideal convergent double sequences of sigma-bounded variation over n-normed spaces

2018 ◽  
Vol 5 (1) ◽  
pp. 1460029
Author(s):  
Vakeel A. Khan ◽  
Kamal M.A.S. Alshlool ◽  
Sameera A.A. Abdullah ◽  
Rami K.A. Rababah ◽  
Ayaz Ahmad ◽  
...  
Keyword(s):  
Bounded Variation ◽  
Double Sequences ◽  
Normed Spaces

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

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