scholarly journals A new sequence space of order α and modulus function

2021 ◽  
Author(s):  
Ekrem Savaş
Keyword(s):  
Sequence Space ◽  
Modulus Function

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.

scholarly journals On Casaro Sequence Space of Fuzzy Numbers Defined by a Modulus Function

OALib ◽  
2014 ◽  
Vol 01 (06) ◽  
pp. 1-6
Author(s):  
Ayhan Esi ◽  
Vakeel A. Khan
Keyword(s):  
Sequence Space ◽  
Fuzzy Numbers ◽  
Modulus Function

Sequence spaces defined by a modulus

1986 ◽  
Vol 100 (1) ◽  
pp. 161-166 ◽  
Author(s):  
I. J. Maddox
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Finite Sequences ◽  
Image Position ◽  
Unit Vectors

Ruckle[4] used the idea of a modulus function ƒ (see Definition 1 below) to construct the sequence spaceThis space is an FK space, and Ruckle proved that the intersection of all such L(f) spaces is ø, the space of finite sequences, thereby answering negatively a question of A. Wilansky: ‘Is there a smallest FK-space in which the set {e1, e2, …} of unit vectors is bounded?’

scholarly journals On a class of generalized difference sequence space definedby modulus function

2005 ◽  
Vol 34 (3) ◽  
pp. 667-677
Author(s):  
Binod Chandra TRIPATHY ◽  
Sabita MAHANTA ◽  
Mikail ET
Keyword(s):  
Sequence Space ◽  
Modulus Function ◽  
Difference Sequence ◽  
Difference Sequence Space

scholarly journals The sequence space $ F (X_{k}, f, p, s) $ on seminormed spaces

2009 ◽  
Vol 40 (3) ◽  
pp. 247-256
Author(s):  
Vinod K. Bhardwaj ◽  
Indu Bala
Keyword(s):  
Sequence Space ◽  
Modulus Function ◽  
Topological Properties ◽  
Vector Valued

The object of this paper is to introduce the vector valued sequence space $F(X_{k}, f, p, s)$ using a modulus function $f$. Various algebraic and topological properties of this space have been investigated. Our results generalize and unify the corresponding earlier results of Ghosh and Srivastava [4], Maddox [10].

scholarly journals Arithmetic convergent sequence space defined by modulus function

2018 ◽  
Vol 37 (4) ◽  
pp. 129-135 ◽  
Author(s):  
Taja Yaying ◽  
Bipan Hazarika
Keyword(s):  
Sequence Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Topological Properties ◽  
Inclusion Results

The aim of this article is to introduce the sequence spaces $AC(f)$ and $AS(f)$ using arithmetic convergence and modulus function, and study algebraic and topological properties of this space, and certain inclusion results.

scholarly journals Properties of $\Gamma^{2}$ defined by a modulus function

2012 ◽  
Vol 31 (1) ◽  
pp. 193
Author(s):  
Chinnswamy Murugesan ◽  
Nagarajan Subramanian
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Modulus Function ◽  
Double Sequence Spaces

In this article, we introduces the generalized difference paranormed double sequence spaces $\Gamma^{2}\left(\Delta^{m}_{\gamma},f,p,q,s\right)$ and $\Lambda^{2} \left(\Delta^{m}_{\gamma},f,p,q,s\right)$ defined over a seminormed sequence space  $\left(X,q\right)$

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