Nonnegative Infinite Matrices that Preserve (p,q)-Convexity of Sequences

Matrix Transformations ◽

Infinite Matrix ◽

Infinite Matrices ◽

This paper deals with matrix transformations that preserve the (p,q)-convexity of sequences. The main result gives the necessary and sufficient conditions for a nonnegative infinite matrix A to preserve the (p,q)-convexity of sequences. Further, we give examples of such matrices for different values of p and q.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

Mathematica Slovaca ◽

10.1515/ms-2021-0059 ◽

2021 ◽

Vol 71 (6) ◽

pp. 1375-1400

Author(s):

Feyzi Başar ◽

Hadi Roopaei

Keyword(s):

Lower Bound ◽

Sequence Space ◽

Sufficient Conditions ◽

Matrix Transformations ◽

Infinite Matrix ◽

The Matrix ◽

Alpha Beta ◽

Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

The Scientific World JOURNAL ◽

10.1155/2014/705818 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Uğur Kadak ◽

Hakan Efe

Keyword(s):

Linear Operator ◽

Sufficient Conditions ◽

Sequence Spaces ◽

General Linear ◽

Matrix Transformations ◽

Infinite Matrix ◽

Complex Field ◽

Infinite Matrices ◽

The Matrix ◽

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the fieldC*and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets overC*to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.

A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171295000871 ◽

1995 ◽

Vol 18 (4) ◽

pp. 681-688 ◽

Cited By ~ 5

Author(s):

B. Choudhary ◽

S. K. Mishra

Keyword(s):

Sufficient Conditions ◽

Sequence Spaces ◽

Matrix Transformations ◽

In this paper we define the sequence spacesSℓ∞(p),Sc(p)andSc0(p)and determine the Köthe-Toeplitz duals ofSℓ∞(p). We also obtain necessary and sufficient conditions for a matrixAto mapSℓ∞(p)toℓ∞and investigate some related problems.

On the Riesz Almost Convergent Sequences Space

Abstract and Applied Analysis ◽

10.1155/2012/691694 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Cited By ~ 11

Author(s):

Mehmet Şengönül ◽

Kuddusi Kayaduman

Keyword(s):

Sequence Space ◽

Sufficient Conditions ◽

Riesz Transforms ◽

Infinite Matrices ◽

Convergent Sequences

The purpose of this paper is to introduce new spaces and that consist of all sequences whose Riesz transforms of order one are in the spaces and , respectively. We also show that and are linearly isomorphic to the spaces and , respectively. The and duals of the spaces and are computed. Furthermore, the classes and of infinite matrices are characterized for any given sequence space and determine the necessary and sufficient conditions on a matrix to satisfy , for all .

Matrix transformations of starshaped sequences

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120100686x ◽

2001 ◽

Vol 28 (4) ◽

pp. 189-200

Author(s):

Chikkanna R. Selvaraj ◽

Suguna Selvaraj

Keyword(s):

Sufficient Conditions ◽

Triangular Matrix ◽

Matrix Transformations ◽

Lower Triangular Matrix ◽

Lower Triangular ◽

We deal with matrix transformations preserving the starshape of sequences. The main result gives the necessary and sufficient conditions for a lower triangular matrixAto preserve the starshape of sequences. Also, we discuss the nature of the mappings of starshaped sequences by some classical matrices.

On the generalized Riesz B-difference sequence spaces

Filomat ◽

10.2298/fil1004035b ◽

2010 ◽

Vol 24 (4) ◽

pp. 35-52 ◽

Cited By ~ 13

Author(s):

Metin Başarir

Keyword(s):

Sufficient Conditions ◽

Sequence Spaces ◽

Matrix Transformations ◽

Difference Sequence ◽

Topological Properties ◽

Linear Spaces ◽

The Matrix ◽

Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

ON MATRIX SEQUENCES ON $cs$ AND $bs$

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.27.1996.4340 ◽

1997 ◽

Vol 27 (3) ◽

pp. 243-246

Author(s):

METIN BASARIR ◽

MIKAIL ET

Keyword(s):

Sufficient Conditions ◽

Double Series ◽

Infinite Matrices ◽

Linear Spaces ◽

We respectively denote the linear spaces of bounded double se- quences and bounded double series by M and BS and denote the usual linear spaces of convergent single series and bounded single series by cs and bs. We determine the necessary and sufficient conditions on the sequence $\mathcal{A} = (\mathcal{A}_p)$ of infinite matrices in the classes $(cs, M)$, $(bs, M)$, $(cs, BS)$ and $(bs, BS)$.

Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171200003732 ◽

2000 ◽

Vol 24 (8) ◽

pp. 533-538

Author(s):

Jinlu Li

Keyword(s):

Classical Result ◽

Sufficient Conditions ◽

Convergent Series ◽

Matrix Transformations ◽

Weighted Mean ◽

Summability Methods ◽

Convergent Sequences

We prove the necessary and sufficient conditions for an infinity matrix to be a mapping, from absolutely convergent series to convergent sequences, which is treated as general weighted mean summability methods. The results include a classical result by Hardy and another by Moricz and Rhoades as particular cases.

Matrix transformations between the sequence space BVP and certain BK spaces

Bulletin Classe des sciences mathematiques et natturalles ◽

10.2298/bmat0227033m ◽

2002 ◽

Vol 123 (27) ◽

pp. 33-46 ◽

Cited By ~ 11

Author(s):

Eberhard Malkowsky ◽

Vladimir Rakocevic ◽

Snezana Zivkovic-Zlatanovic

Keyword(s):

Linear Operator ◽

Hausdorff Measure ◽

Sequence Space ◽

Measure Of Noncompactness ◽

Sufficient Conditions ◽

Matrix Transformations ◽

Hausdorff Measure Of Noncompactness ◽

Bk Spaces

In this paper, we characterize matrix transformations between the sequence space bvp (1 < p < ?) and certain BK spaces. Further?more, we apply the Hausdorff measure of noncompactness to give necessary and sufficient conditions for a linear operator between these spaces to be compact.

The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.