scholarly journals Completeness of Sequence Spaces Generated by an Orlicz Function

2019 ◽  
Vol 19 (1) ◽  
pp. 1-14
Author(s):  
Nur Khusnussaadah ◽  
S. Supama
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Orlicz Sequence Space ◽  
Complete Space ◽  
Summable Sequence ◽  
Norm Space ◽  
The Relationship ◽  
Convergence Sequence

In this paper, we discuss about completeness property of Orlicz sequence spaces defined by an Orlicz function. Orlicz sequence space is generalization of p-summable sequence space, for every   which is also an Orlicz sequence space. Based on the property of convergence sequence on norm space, we define $\Phi$-convergence sequence on Orlicz sequence space. Moreover, we define $\Phi$-Cauchy sequence and $\Phi$-complete on Orlicz sequence space. In this paper, we show the relationship between the (ordinary) convergent sequence, $\Phi$-convergent and $\Phi$-Cauchy sequences. Finally, it will also be shown that Orlicz sequence space is Banach space and $\Phi$-complete 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 On Paranormed Ideal Convergent Generalized Difference Strongly Summable Sequence Spaces Defined over n-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Bipan Hazarika
Keyword(s):  
Difference Operator ◽  
Orlicz Function ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Topological Structures ◽  
New Class ◽  
Summable Sequence

We introduce a new class of ideal convergent (shortly I-convergent) sequence spaces using an Orlicz function and difference operator of order defined over the n-normed spaces. We investigate these spaces for some linear topological structures. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces. We also give some relations related to these sequence 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.

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 A study of Nörlund ideal convergent sequence spaces

2020 ◽  
pp. 44-44
Author(s):  
Vakeel Khan ◽  
Sameera Abdullah ◽  
Kamal Alshlool
Keyword(s):  
Sequence Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Ideal Convergence ◽  
Algebraic Properties

The N?rlund matrix Nt in the theory of sequence space was firstly used by Wang. In this paper, by using the N?rlund mean Nt and the notion of ideal convergence, we introduce some new sequence spaces cI 0(Nt), cI (Nt), and `I 1(Nt) as a domain of N?rlund mean. We study some topological and algebraic properties on these spaces. Further, some inclusion concerning these spaces are discussed.

scholarly journals On some double almost lacunary sequence spaces defined by Orlicz functions

Filomat ◽  
2005 ◽  
pp. 35-44 ◽  
Author(s):  
Ekrem Savas ◽  
Richard Patterson
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Orlicz Function ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Orlicz Functions ◽  
Lacunary Statistical Convergence

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.

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