scholarly journals Regular matrix transformation on triple sequence spaces - I

Mathematica ◽  
2018 ◽  
Vol 60 (83) (2) ◽  
pp. 127-139
Author(s):  
Shyamal Debnath ◽  
◽  
Bimal Chandra Das ◽  
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformation ◽  
Regular Matrix

scholarly journals Regular matrix transformation on triple sequence spaces

2017 ◽  
Vol 35 (1) ◽  
pp. 85 ◽  
Author(s):  
Shyamal Debnath ◽  
Bimal Chandra Das
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Sufficient Condition ◽  
Regular Matrix ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The main aim of this paper is to introduce the necessary and sufficient condition for a particular type of transformation of the form A: (a......)  be regular from a triple sequence space to another triple sequence space. 

scholarly journals On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Point Spectrum ◽  
Sequence Spaces ◽  
Matrix Operator ◽  
Regular Matrix ◽  
Approximate Point Spectrum ◽  
Fine Spectrum ◽  
New Development ◽  
The Matrix ◽  
Convergent Sequences

The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces andc. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces andc. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.

Convergence field of Abel’s summation method

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Peter Letavaj
Keyword(s):  
Metric Space ◽  
Linear Subspace ◽  
Summation Method ◽  
Matrix Transformation ◽  
Matrix Transformations ◽  
Regular Matrix ◽  
Porous Set ◽  
Linear Metric Space ◽  
Bounded Sequences

AbstractLet F(A) denote the set of all bounded sequences summable by Abel’s method. It is known, that F(A) is a linear subspace of the linear metric space (S, ρ) of all bounded sequences endowed with the sup metric. It is shown in [KOSTYRKO, P.: Convergence fields of regular matrix transformations 2, Tatra Mt. Math. Publ. 40 (2008), 143–147] that the convergence field of a regular matrix transformation is a σ-porous set. We show that F(A) is very porous in S.

scholarly journals New matrix domain derived by the matrix product

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan
Keyword(s):  
Topological Structure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Matrix Product ◽  
Difference Matrix ◽  
Matrix Domain ◽  
The Matrix ◽  
Necessary And Sufficient

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ?- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c,??.

Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence

2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma
Keyword(s):  
Statistical Convergence ◽  
Orlicz Function ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Regular Matrix ◽  
Normed Spaces ◽  
Double Sequence Spaces ◽  
Inclusion Relations ◽  
Algebraic Properties

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.

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