Some geometric properties of a new difference sequence space defined by de la Vallée-Poussin mean

2014 ◽  
Vol 234 ◽  
pp. 237-244 ◽  
Author(s):  
Mikail Et ◽  
Murat Karakaş ◽  
Vatan Karakaya
Keyword(s):  
Sequence Space ◽  
Difference Sequence ◽  
Geometric Properties ◽  
Difference Sequence Space ◽  
De La Vallée Poussin

scholarly journals Some Topological and Geometrical Properties of a New Difference Sequence Space

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Serkan Demiriz ◽  
Celal Çakan
Keyword(s):  
Sequence Space ◽  
Final Section ◽  
Difference Sequence ◽  
Geometric Properties ◽  
Geometrical Properties ◽  
Difference Sequence Space ◽  
Bk Space

We introduce the new difference sequence space . Further, it is proved that the space is the BK-space including the space , which is the space of sequences of pbounded variation. We also show that the spaces , and are linearly isomorphic for . Furthermore, the basis and the , and duals of the space are determined. We devote the final section of the paper to examine some geometric properties of the space .

SOME DIFFERENCE SEQUENCE SPACES GENERATED BY DE LA VALLÉE-POUSSIN MEAN

2013 ◽  
Vol 06 (02) ◽  
pp. 1350018
Author(s):  
P. D. Srivastava ◽  
Atanu Manna
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Modular Structure ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
De La Vallée Poussin ◽  
Difference Sequence Spaces

A difference sequence space using φ-function and involving the concept of de la Vallée-Poussin mean is introduced. Inclusion relations, structural and topological properties of this space are investigated. By introducing a modular structure, the equality of the countably and uniformly countably modulared spaces is obtained.

On the paranormed Nörlund difference sequence space of fractional order and geometric properties

2021 ◽  
Vol 71 (1) ◽  
pp. 155-170
Author(s):  
Taja Yaying
Keyword(s):  
Fractional Order ◽  
Sequence Space ◽  
Difference Operator ◽  
Difference Sequence ◽  
Topological Properties ◽  
Fractional Difference ◽  
Geometric Properties ◽  
Nörlund Matrix ◽  
Difference Sequence Space ◽  
New Space

Abstract In this article we introduce paranormed Nörlund difference sequence space of fractional order α, Nt (p, Δ(α)) defined by the composition of fractional difference operator Δ(α), defined by ( Δ ( α ) x ) k = ∑ i = 0 ∞ ( − 1 ) i Γ ( α + 1 ) i ! Γ ( α − i + 1 ) x k − i , $\begin{array}{} \displaystyle (\Delta^{(\alpha)}x)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i}, \end{array}$ and Nörlund matrix Nt . We give some topological properties, obtain the Schauder basis and determine the α−, β− and γ-duals of the new space. We characterize certain matrix classes related to this new space. Finally we investigate certain geometric properties of the space Nt (p, Δ(α)).

scholarly journals Multiplication Operators on Orlicz Generalized Difference (sss)

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Multiplication Operators ◽  
Difference Sequence ◽  
Geometrical Structures ◽  
Difference Sequence Space

In this article, we inspect the sufficient conditions on the Orlicz generalized difference sequence space to be premodular Banach (sss). We look at some topological and geometrical structures of the multiplication operators described on Orlicz generalized difference prequasi normed (sss).

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