scholarly journals On Some Lacunary Generalized Difference Sequence Spaces of Invariant Means De ned by a Sequence of Modulus Function

2011 ◽  
Vol 51 (4) ◽  
pp. 385-393
Author(s):  
Gulcan Atici ◽  
Cigdem Asma Bektas
Keyword(s):  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Invariant Means ◽  
Difference Sequence Spaces

scholarly journals Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Sudhir Kumar ◽  
Vijay Kumar ◽  
S. S. Bhatia
Keyword(s):  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Topological Properties ◽  
Ideal Convergence ◽  
Difference Sequences ◽  
Invariant Means ◽  
Difference Sequence Spaces

The main objective of this paper is to introduce a new kind of sequence spaces by combining the concepts of modulus function, invariant means, difference sequences, and ideal convergence. We also examine some topological properties of the resulting sequence spaces. Further, we introduce a new concept of SθσΔm(I)-convergence and obtain a condition under which this convergence coincides with above-mentioned sequence spaces.

scholarly journals On some generalized difference sequences with respect to a modulus function

Filomat ◽  
2003 ◽  
pp. 23-33 ◽  
Author(s):  
Mikail Et ◽  
Yavuz Altin ◽  
Hifsi Altinok
Keyword(s):  
Banach Space ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, ?, f, p]0 (?r, E), [V, ?, f, p]1 (?r, E), [V, ?, f, p]? (?r, E) S? (?r, E) and S?0 (?r, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space S? (?r, E) may be represented as a [V, ?, f, p]1 (?r, E)space.

scholarly journals Some generalized difference sequence spaces of invariant means defined by Orlicz functions

2005 ◽  
Vol 2005 (11) ◽  
pp. 1713-1722
Author(s):  
Ahmad H. A. Bataineh ◽  
Laith E. Azar
Keyword(s):  
Sequence Spaces ◽  
Difference Sequence ◽  
Orlicz Functions ◽  
Delta Sigma ◽  
Inclusion Relations ◽  
Invariant Means ◽  
Difference Sequence Spaces

We define the sequence spaces[wθ,M,p,u,Δ]σ,[wθ,M,p,u,Δ]σ0, and[wθ,M,p,u,Δ]σ∞which are defined by combining the concepts of Orlicz functions, invariant means, and lacunary convergence. We also study some inclusion relations and linearity properties of the above-mentioned spaces. These are generalizations of those defined and studied by Savaş and Rhoades in 2002 and some others before.

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