scholarly journals On double sequence spaces defined by an Orlicz function on a seminormed space

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 631-638 ◽  
Author(s):  
Ekrem Savaş ◽  
Eren Savaş
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequence Spaces ◽  
Double Sequence Space ◽  
Seminormed Space ◽  
Inclusion Results

In this paper we introduce and study the double sequence space m''(M,?,q) by using the Orlicz function M. Also we obtain some inclusion results involving the space m''(M,?,q).

scholarly journals Vector valued paranormed statistically convergent double sequence spaces

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
Binod Tripathy ◽  
Bipul Sarma
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequence Spaces ◽  
Seminormed Space ◽  
Vector Valued ◽  
Inclusion Results

AbstractIn this article we introduce the vector valued paranormed sequence spaces $${}_2\overline c (q,p), {}_2\overline c _0 (q,p), ({}_2\overline c )^B (q,p), ({}_2\overline c _0 )^B (q,p), ({}_2\overline c )^R (q,p)$$ and $$({}_2\overline c _0 )^R (q,p)$$ defined over a seminormed space (X,q). We study their different properties like completeness, solidness, symmetry, convergence freeness etc. We prove some inclusion results.

Vector valued double sequence spaces defined by Orlicz function

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
Binod Tripathy ◽  
Bipul Sarma
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequence Spaces ◽  
Vector Valued ◽  
Inclusion Results

AbstractIn this article we introduce some vector valued double sequence spaces defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

scholarly journals Matrix summability of statistically p-convergence sequences

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 55-62 ◽  
Author(s):  
Richard Patterson ◽  
Ekrem Savaş
Keyword(s):  
Sequence Space ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Arbitrary Sequence ◽  
Regular Matrix ◽  
Multidimensional Analog ◽  
Matrix Summability ◽  
Double Sequence Spaces ◽  
Double Sequence Space

Matrix summability is arguable the most important tool used to characterize sequence spaces. In 1993 Kolk presented such a characterization for statistically convergent sequence space using nonnegative regular matrix. The goal of this paper is extended Kolk?s results to double sequence spaces via four dimensional matrix transformation. To accomplish this goal we begin by presenting the following multidimensional analog of Kolk?s Theorem : Let X be a section-closed double sequence space containing e'' and Y an arbitrary sequence space. Then B ?(st2A ? X,Y) if and only if B ? (c''? X,Y) and B[KxK]?(X,Y) (?A(K?K)=0). In addition, to this result we shall also present implication and variation of this theorem.

On paranorm BVσ I-convergent double sequence spaces defined by an Orlicz function

Analysis ◽  
2017 ◽  
Vol 37 (3) ◽  
Author(s):  
Vakeel A. Khan ◽  
Hira Fatima ◽  
Sameera A. A. Abdullah ◽  
Kamal M. A. S. Alshlool
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequence Spaces

AbstractThe space

scholarly journals Some New Double-Sequence Spaces in 2-Normed Spaces Defined by Ideal Convergence and an Orlicz Function

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Orhan Tug ◽  
Mutlay Dogan ◽  
Abdullah Kurudirek
Keyword(s):  
Orlicz Function ◽  
Double Sequence ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Double Sequence Spaces ◽  
Difference Sequence Spaces

We generalize some sequence spaces from single to double, we study some topological properties of these double sequence spaces by using ideal convergence, difference sequence spaces, and an Orlicz function in 2-normed spaces, and we give some results related to these sequence spaces.

scholarly journals Some Double Sequence Spaces of Fuzzy Real Numbers of Paranormed Type

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Bipul Sarma
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Real Numbers ◽  
Double Sequence Spaces ◽  
Fuzzy Real Numbers ◽  
Sequence Algebra ◽  
Inclusion Results

We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. We prove some inclusion results too.

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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