scholarly journals Some new sequence spaces defined by lacunary sequences

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Ekrem Savas ◽  
Vatan Karakaya
Keyword(s):  
Bounded Variation ◽  
Sequence Spaces ◽  
Almost Convergence ◽  
Lacunary Sequences

AbstractIt is natural to expect that lacunary almost convergence must be related to the some concept of lacunary almost bounded variations in the some view as almost convergence is related to almost bounded variation. The purpose of this paper is to examine this new concept in some details. Some inclusion theorems have been established.

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 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 Some sequence spaces and almost convergence

1976 ◽  
Vol 22 (4) ◽  
pp. 446-455 ◽  
Author(s):  
Sudarsan Nanda
Keyword(s):  
Strong Summability ◽  
Sequence Spaces ◽  
Almost Convergence ◽  
Inclusion Relations ◽  
Generalized Limits

AbstractIn this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper is to introduce the spaces of strongly almost summable sequences which happen to be complete paranormed spaces under certain conditions. Some topological results, characterisation of strongly almost regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed.

scholarly journals On some spaces of summable sequences and their duals

1986 ◽  
Vol 9 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Geraldo Soares de Souza ◽  
G. O. Golightly
Keyword(s):  
Bounded Variation ◽  
Dual Space ◽  
Sequence Spaces ◽  
Simple Argument

Suppose thatSis the space of all summable sequencesαwith‖α‖S=supn≥0|∑j=n∞αj|andJthe space of all sequencesβof bounded variation with‖β‖J=|β0|+∑j=1∞|βj−βj−1|. Then forαinSandβinJ |∑j=0∞αjβj|≤‖α‖S‖β‖J; this inequality leads to the description of the dual space ofSasJ. It, related inequalities, and their consequences are the content of this paper. In particular, the inequality cited above leads directly to the Stolz form of Abel's theorem and provides a very simple argument. Also, some other sequence spaces are discussed.

scholarly journals On almost p-bounded variation of lacunary sequences

2011 ◽  
Vol 61 (6) ◽  
pp. 1502-1506 ◽  
Author(s):  
Vatan Karakaya ◽  
Ekrem Savas
Keyword(s):  
Bounded Variation ◽  
Lacunary Sequences

scholarly journals Some sequence spaces and absolute almost convergence

1984 ◽  
Vol 283 (2) ◽  
pp. 729-729 ◽  
Author(s):  
G. Das ◽  
B. Kuttner ◽  
S. Nanda
Keyword(s):  
Sequence Spaces ◽  
Almost Convergence

scholarly journals Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Ugur Kadak
Keyword(s):  
Fractional Order ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Fixed Sequence ◽  
Related Sequence ◽  
Lacunary Sequences ◽  
Lacunary Statistical Convergence ◽  
Inclusion Relations ◽  
The Relationship ◽  
Difference Sequence Spaces

We generalize the lacunary statistical convergence by introducing the generalized difference operatorΔναof fractional order, whereαis a proper fraction andν=(νk)is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.

scholarly journals Some new sequence spaces and almost convergence

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 59-64 ◽  
Author(s):  
Sameer Gupkari
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Almost Convergence ◽  
Infinite Matrices

The sequence space arc have been defined and the classes (arc : lp) and (arc : c) of infinite matrices have been characterized by Aydin and Ba?ar (On the new sequence spaces which include the spaces c0 and c, Hokkaido Math. J. 33(2) (2004), 383-398) [1], where 1 ? p ? ?. The main purpose of the present paper is to characterize the classes (arc : f) and (arc : f0), where f and f0 denote the spaces of almost convergent and almost convergent null sequences with real or complex terms. .

scholarly journals On Some Lacunary Almost Convergent Double Sequence Spaces and Banach Limits

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Metin Başarır ◽  
Şükran Konca
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Almost Convergence ◽  
Double Sequences ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Banach Limits ◽  
Sublinear Functionals

The object of this paper is to introduce some new sequence spaces related with the concept of lacunary strong almost convergence for double sequences and also to characterize these spaces through sublinear functionals that both dominate and generate Banach limits and to establish some inclusion relations.

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