scholarly journals Some new sequence spaces defined by bounded variation in 2-normed spaces

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 483-492
Author(s):  
Ekrem Savaş
Keyword(s):  
Bounded Variation ◽  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Algebraic Properties

In this paper, by using Orlicz function and almost lacunary bounded variation we introduce and examine a new sequence space in 2-normed spaces. We also study some basic topological and algebraic properties of these spaces. In addition, we shall established inclusion theorems between these sequence spaces.

Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence

2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Normed Spaces ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.

Λ-strongly summable sequence spaces in n-normed spaces defined by ideal convergence and an Orlicz function

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Ayhan Esi ◽  
M. Kemal Özdemir
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Summable Sequence ◽  
Inclusion Results

AbstractIn this paper we introduce some certain new sequence spaces via ideal convergence, λ-sequence and an Orlicz function in n-normed spaces and study different properties of these spaces and also establish some inclusion results among them.

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.

scholarly journals On some new modular sequence spaces

2013 ◽  
Vol 31 (2) ◽  
pp. 55 ◽  
Author(s):  
Cigdem Asma Bektas ◽  
Gülcan Atıci
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Orlicz Sequence Space ◽  
Orlicz Functions ◽  
Orlicz Sequence Spaces

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ℓM which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of ℓ (M), which is an AK-space, is the space h (M) . We define the sequence spaces ℓM (m) and ℓ N(m), where M = (Mk) and N = (Nk) are sequences of Orlicz functions such that Mk and Nk be mutually  complementary for each k. We also examine some topological properties of these spaces. We give the α−, β− and γ− duals of the sequence space h (M) and α− duals of the squence spaces ℓ (M, λ) and ℓ (N, λ).

scholarly journals Applications of double lacunary sequences to n-norm

2015 ◽  
Vol 7 (1) ◽  
pp. 67-88
Author(s):  
Kuldip Raj ◽  
Sunil Kumar Sharma
Keyword(s):  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Inclusion Relation ◽  
Normed Spaces ◽  
Lacunary Sequences ◽  
Double Lacunary Sequence

AbstractIn the present paper we define some classes of double lacunary sequence spaces over n-normed spaces by means of a Musielak- Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relation among the classes are also examined.

scholarly journals Generalized Differenceλ-Sequence Spaces Defined by Ideal Convergence and the Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
The Ideal

We introduced the ideal convergence of generalized difference sequence spaces combining an infinite matrix of complex numbers with respect toλ-sequences and the Musielak-Orlicz function overn-normed spaces. We also studied some topological properties and inclusion relations between these spaces.

scholarly journals Sequence Spaces Defined by Musielak-Orlicz Function over -Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
A. Kılıçman
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Normed Spaces ◽  
Inclusion Relations

In the present paper we introduce some sequence spaces overn-normed spaces defined by a Musielak-Orlicz function . We also study some topological properties and prove some inclusion relations between these spaces.

scholarly journals Some New Double-Sequence Spaces in 2-Normed Spaces Defined by Ideal Convergence and an Orlicz Function

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Orhan Tug ◽  
Mutlay Dogan ◽  
Abdullah Kurudirek
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Double Sequence Spaces ◽  
Difference Sequence Spaces

We generalize some sequence spaces from single to double, we study some topological properties of these double sequence spaces by using ideal convergence, difference sequence spaces, and an Orlicz function in 2-normed spaces, and we give some results related to these sequence spaces.

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