scholarly journals Sequence spaces defined via Euler method and matrix transformations

2021 ◽  
Author(s):  
Pranav Sharma
Keyword(s):  
Normed Space ◽  
Lacunary Sequence ◽  
Euler Method ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Matrix Summability ◽  
Inclusion Relations ◽  
Transformation Methods

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

scholarly journals Sequence spaces defined via Euler method and matrix transformations

2021 ◽  
Vol 40 (5) ◽  
pp. 1137-1145
Author(s):  
Pranav Sharma
Keyword(s):  
Normed Space ◽  
Lacunary Sequence ◽  
Euler Method ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Matrix Summability ◽  
Inclusion Relations ◽  
Transformation Methods

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

2020 ◽  
Vol 26 (2) ◽  
pp. 173-183
Author(s):  
Kuldip Raj ◽  
Kavita Saini ◽  
Anu Choudhary
Keyword(s):  
Difference Operator ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Normed Spaces ◽  
Fractional Difference ◽  
New Approach ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Bounded Sequences

AbstractRecently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

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 New Difference Sequence Spaces Defined by Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
S. A. Mohiuddine ◽  
A. Kılıçman
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

scholarly journals On the Domain of the Triangle on the Spaces of Null, Convergent, and Bounded Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Naim L. Braha ◽  
Feyzi Başar
Keyword(s):  
Type Theorem ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Bounded Sequences ◽  
Convergent Sequences

We introduce the spaces of -null, -convergent, and -bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute -, -, and -duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of -bounded and -convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.

scholarly journals Almost Sequence Spaces Derived by the Domain of the Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ali Karaisa ◽  
Ümıt Karabıyık
Keyword(s):  
Normed Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Classes ◽  
Almost Convergent Sequence ◽  
Inclusion Relations ◽  
The Matrix

By using , we introduce the sequence spaces , , and of normed space and -space and prove that , and are linearly isomorphic to the sequence spaces , , and , respectively. Further, we give some inclusion relations concerning the spaces , , and the nonexistence of Schauder basis of the spaces and is shown. Finally, we determine the - and -duals of the spaces and . Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.

scholarly journals On Some Properties of New Paranormed Sequence Space of Nonabsolute Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
The Other ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Paranormed Sequence Space ◽  
Inclusion Relations

We introduce some new generalized sequence space related to the space . Furthermore we investigate some topological properties as the completeness, the isomorphism, and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute -, -, and -duals of this space and characterize certain matrix transformations on this sequence space.

scholarly journals On the spaces of Nörlund almost null and Nörlund almost convergent sequences

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 773-783 ◽  
Author(s):  
Orhan Tuğ ◽  
Feyzi Başar
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

In this article, the sequence spaces f0(Nt) and f (Nt) are introduced as the domain of N?rlund mean in the spaces f0 and f of almost null and almost convergent sequences which are isomorphic to the spaces f0 and f , respectively, and some inclusion relations are given. Additionally, alpha, beta and gamma duals of the sequence spaces f0(Nt) and f (Nt) are determined. Finally, the classes (?(Nt):?) and (?:?(Nt)) of matrix transformations are characterized for given sequence spaces ? and ? together with two Steinhaus type results.

scholarly journals On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 33-51 ◽  
Author(s):  
M. Mursaleen ◽  
Abdullah Noman
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Bk Space

In the present paper, we introduce the sequence space l?p of non-absolute type and prove that the spaces ??p and lp are linearly isomorphic for 0 < p ? ?. Further, we show that ??p is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ? p ? ?, respectively. Furthermore, we derive some inclusion relations concerning the space ??p. Finally, we construct the basis for the space ??p, where 1 ? p < ?.

scholarly journals On Generalized Difference Hahn Sequence Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Kuldip Raj ◽  
Adem Kiliçman
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Inclusion Relations

We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaceshpℱ,u,Δrare investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.

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