scholarly journals Extension of lacunary statistical convergence on vector valued double difference sequence space

2014 ◽  
Vol 7 (1) ◽  
pp. 19-30
Author(s):  
Anindita Basu
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Double Difference ◽  
Difference Sequence ◽  
Lacunary Statistical Convergence ◽  
Difference Sequence Space ◽  
Vector Valued

On New Difference Sequence Space and Their Generalised Almost Statistical Convergence

2020 ◽  
pp. 212-219
Author(s):  
Ajaya Kumar Singh
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Convergent Sequence ◽  
Difference Sequence ◽  
Almost Convergence ◽  
Topological Properties ◽  
Statistical Limit ◽  
Difference Sequence Space ◽  
Limit Functional ◽  
Convergent Sequences

The object of the present paper is to introduce the notion of generalised almost statistical (GAS) convergence of bounded real sequences, which generalises the notion of almost convergence as well as statistical convergence of bounded real sequences. We also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Also, the existence GAS convergent sequence, which is neither statistical convergent nor almost convergent. Lastly, some topological properties of the space of all GAS convergent sequences are investigated.

scholarly journals On Vector-Valued Generalized Lorentz Difference Sequence Space

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Birsen Sağır ◽  
Oğuz Oğur
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Inclusion Relations ◽  
Difference Sequence Space ◽  
Vector Valued ◽  
Difference Sequence Spaces

We introduce generalized Lorentz difference sequence spaces d(v,Δ,p). Also we study some topologic properties of this space and obtain some inclusion relations.

scholarly journals Multiplication Operators on Orlicz Generalized Difference (sss)

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Multiplication Operators ◽  
Difference Sequence ◽  
Geometrical Structures ◽  
Difference Sequence Space

In this article, we inspect the sufficient conditions on the Orlicz generalized difference sequence space to be premodular Banach (sss). We look at some topological and geometrical structures of the multiplication operators described on Orlicz generalized difference prequasi normed (sss).

scholarly journals Generalized vector valued double sequence space using modulus function

2007 ◽  
Vol 38 (4) ◽  
pp. 347-366
Author(s):  
Anindita Basu ◽  
P. D. Srivastava
Keyword(s):  
Sequence Space ◽  
Statistical Convergence ◽  
Double Sequence ◽  
Modulus Function ◽  
Real Numbers ◽  
Double Sequence Space ◽  
Seminormed Space ◽  
Vector Valued

In this paper, we introduce a generalized vector valued paranormed double sequence space $ F^{2}(E,p,f,s) $, using modulus function $ f $, where $ p=(p_{nk}) $ is a sequence of non-negative real numbers, $ s\geq 0 $ and the elements are chosen from a seminormed space $ (E, q_{E}) $. Results regarding completeness, normality, $ K_{2} $-space, co-ordinatewise convergence etc. are derived. Further, a study of multiplier sets, ideals, notion of statistical convergence and ($ p_{nk} $ )-Ces\'aro summability in the space $ F^{2}(E,p,f,s) $ is also made.

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