\mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces

LetA=(ank)be an infinite matrix with allank≥0andPa bounded, positive real sequence. For normed spacesEandEkthe matrixAgenerates paranormed sequence spaces such as[A,P]∞((Ek)),[A,P]0((Ek)), and[A,P](E)which generalize almost all the existing sequence spaces, such asl∞,c0,c,lp,wp, and several others. In this paper, conditions under which these three paranormed spaces are separable, complete, andr-convex, are established.

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Some Vector Valued Sequence Spaces Generated by Musielak- Phy Function Over 2-Normed Spaces

Journal of Research in Mathematics Trends and Technology ◽

10.32734/jormtt.v1i2.2837 ◽

2019 ◽

Vol 1 (2) ◽

pp. 50-55

Author(s):

M Ofie

Keyword(s):

Sequence Spaces ◽

Normed Spaces ◽

Vector Valued

In this work, we introduced some new vector valued sequence spaces over 2-normed spaces using Musielak-Phy function Φ = (𝜑 𝑛 ) . We also studied some properties of these spaces.

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On some vector valued multiplier spaces with statistical Cesàro summability

Filomat ◽

10.2298/fil1916135k ◽

2019 ◽

Vol 33 (16) ◽

pp. 5135-5147 ◽

Cited By ~ 1

Author(s):

Ramazan Kama

Keyword(s):

Sequence Spaces ◽

Normed Spaces ◽

Cesàro Summability ◽

Cesaro Summability ◽

Vector Valued ◽

Multiplier Sequence

In the present paper we define and study some vector valued spaces within the frame of the Statistical Ces?ro convergence and the Statistically Ces?ro summability in normed spaces. Also, we characterize the continuous, compact and sequential continuous summing operators on Statistical Ces?ro multiplier sequence spaces.

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Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

Journal of Applied Analysis ◽

10.1515/jaa-2020-2018 ◽

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.

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

Mathematica Slovaca ◽

10.2478/s12175-013-0137-y ◽

2013 ◽

Vol 63 (4) ◽

Cited By ~ 2

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.

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Some sequence spaces and completeness of normed spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2017.03.05 ◽

2017 ◽

Vol 26 (3) ◽

pp. 281-287

Author(s):

RAMAZAN KAMA ◽

◽

BILAL ALTAY ◽

Keyword(s):

Normed Space ◽

Summability Method ◽

Sequence Spaces ◽

Normed Spaces ◽

Cesàro Summability ◽

Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

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