scholarly journals On Some Geometric Properties of a New Paranormed Sequence Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Vatan Karakaya ◽  
Fatma Altun
Keyword(s):  
Sequence Space ◽  
Luxemburg Norm ◽  
Geometric Properties ◽  
Paranormed Sequence Space ◽  
New Space

We introduce a new sequence space which is defined by the operatorW=(wnk)on the sequence spaceℓ(p). We define a modular functional on this space and investigate structure of this space equipped with Luxemburg norm. Also we study some geometric properties which are called Kadec-Klee, k-NUC, and uniform Opial properties and prove that this new space possesses these properties.

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)).

Some topological and geometric properties of generalized Euler sequence space

2010 ◽  
Vol 60 (3) ◽  
Author(s):  
Emrah Kara ◽  
Mahpeyker Öztürk ◽  
Metin Bašarir
Keyword(s):  
Sequence Space ◽  
Southeast Asian ◽  
Sequence Spaces ◽  
Luxemburg Norm ◽  
Geometric Properties

AbstractIn this paper, we introduce the Euler sequence space e r(p) of nonabsolute type and prove that the spaces e r(p) and l(p) are linearly isomorphic. Besides this, we compute the α-, β- and γ-duals of the space e r(p). The results proved herein are analogous to those in [ALTAY, B.—BASŠAR, F.: On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (2002), 701–715] for the Riesz sequence space r q(p). Finally, we define a modular on the Euler sequence space e r(p) and consider it equipped with the Luxemburg norm. We give some relationships between the modular and Luxemburg norm on this space and show that the space e r(p) has property (H) but it is not rotund (R).

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals

2018 ◽  
Vol 68 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Space ◽  
Geometric Properties ◽  
Orlicz Functions ◽  
Opial Property ◽  
Uniform Opial Property ◽  
Vector Valued

AbstractIn the present paper we introduce generalized vector-valued Musielak-Orlicz sequence spacel(A,𝓜,u,p,Δr,∥·,… ,·∥)(X) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators ofs-type and operator ideals by using the sequence ofs-number (in the sense of Pietsch) under certain conditions on matrixA.

scholarly journals Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

2018 ◽  
Vol 36 (1) ◽  
pp. 37 ◽  
Author(s):  
Bipan Hazarika ◽  
Anupam Das
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Band Matrix ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

Sign in / Sign up

Export Citation Format

Share Document