scholarly journals ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX

2020 ◽  
Vol 3 (1) ◽  
pp. 66-76
Author(s):  
Mahmut KARAKUŞ ◽  
Tunay BİLGİN
Keyword(s):  
Summability Matrix

Regular and Mercerian Generalized Lototsky Method

1984 ◽  
Vol 27 (1) ◽  
pp. 65-71 ◽  
Author(s):  
J. F. Miller ◽  
H. B. Skerry
Keyword(s):  
Half Plane ◽  
Matrix Method ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Summability Matrix

AbstractNecessary conditions and sufficient conditions are obtained for the generalized Lototsky summability matrix method (F, dn) to be regular and Mercerian. In particular, a set of conditions equivalent to being regular and Mercerian is given for real {dn} and for complex {dn} eventually in any closed half-plane containing the origin.

scholarly journals Summability methods based on the Riemann Zeta function

1988 ◽  
Vol 11 (1) ◽  
pp. 27-36
Author(s):  
Larry K. Chu
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Necessary Condition ◽  
Real Sequence ◽  
Necessary And Sufficient Condition ◽  
Summability Methods ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Summability Matrix ◽  
Necessary And Sufficient

This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequencexto be zeta summable. A zeta summability matrixZtassociated with a real sequencetis introduced; a necessary and sufficient condition on the sequencetsuch thatZtmapsl1tol1is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.

scholarly journals Four dimensional characterization of bounded double sequences

2004 ◽  
Vol 35 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Richard F. Patterson
Keyword(s):  
Bounded Sequence ◽  
Matrix Transformations ◽  
Double Sequences ◽  
Matrix Methods ◽  
Multidimensional Analog ◽  
Dimensional Matrix ◽  
Important Theorem ◽  
Summability Matrix ◽  
Regular Summability

In 1945 Brudno presented the following important theorem: If $A$ and $B$ are regular summability matrix methods such that every bounded sequence summed by $A$ is also summed by $B$, then it is summed by $B$ to the same value. R. G. Cooke suggested that a simpler proof would be desirable. Petersen presented such a proof. The goal of the paper is to present an accessible multidimensional analog of Brudno theorem for double sequences using four dimensional matrix transformations.

scholarly journals On matrix methods of convergence of order α in (ℓ)-groups

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2069-2077 ◽  
Author(s):  
Antonio Boccuto ◽  
Pratulananda Das
Keyword(s):  
Matrix Method ◽  
Statistical Convergence ◽  
Cauchy Type ◽  
Matrix Methods ◽  
Type Criterion ◽  
Summability Matrix ◽  
Convergent Sequences

We introduce a concept of convergence of order ?, with 0 < ? ? 1, with respect to a summability matrix method A for sequences (which generalizes the notion of statistical convergence of order ?), taking values in (?)-groups. Some main properties and differences with the classical A-convergence are investigated. A Cauchy-type criterion and a closedness result for the space of convergent sequences according our notion is proved.

Summability methods which include the Riesz typical means. II

1971 ◽  
Vol 69 (2) ◽  
pp. 297-300 ◽  
Author(s):  
B. C. Russell
Keyword(s):  
Regular Sequence ◽  
Cesàro Summability ◽  
Convergence Factor ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Factor Theorem ◽  
T Matrix ◽  
Image Position ◽  
Summability Matrix ◽  
Necessary And Sufficient

By making use of a convergence-factor theorem of Bosanquet(3), Cooke((4), Theorem I) gave conditions for a regular sequence-to-sequence summability matrix B to be at least as strong as Cesàro summability (C, κ) (κ > 0), namely:Theorem C. Let κ > 0. In order that the T-matrix B = (bρμ) shall satisfy B ⊇ (C, κ) it is necessary and sufficient thatIf 0 < κ ≤ 1 then (2) alone is necessary and sufficient.

scholarly journals Gap Tauberian theorems

1993 ◽  
Vol 47 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Jeff Connor
Keyword(s):  
Tauberian Theorem ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Weighted Mean ◽  
Tauberian Condition ◽  
Support Set ◽  
Tauberian Conditions ◽  
Summability Matrix ◽  
Regular Summability ◽  
Bk Spaces

In the first section we establish a connection between gap Tauberian conditions and isomorphic copies of Co for perfect coregular conservative BK spaces and in the second we give a characterisation of gap Tauberian conditions for strong summability with respect to a nonnnegative regular summability matrix. These results are used to show that a gap Tauberian condition for strong weighted mean summability is also a gap Tauberian condition for ordinary weighted mean summability. We also make a remark regarding the support set of a matrix and give a Tauberian theorem for a class of conull spaces.

A Voronovskaya-type formula for SMK operators via statistical convergence

2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Ali Aral ◽  
Oktay Duman
Keyword(s):  
Statistical Convergence ◽  
Type Theorem ◽  
Type Formula ◽  
Voronovskaya Type Theorem ◽  
Summability Matrix ◽  
Regular Summability

AbstractIn this paper, we obtain a statistical Voronovskaya-type theorem for the Szász-Mirakjan-Kantorovich (SMK) operators by using the notion of A-statistical convergence, where A is a non-negative regular summability matrix.

scholarly journals A sequence algebra associated with distributions

1978 ◽  
Vol 19 (1) ◽  
pp. 39-49
Author(s):  
G.M. Petersen
Keyword(s):  
New York ◽  
Banach Algebra ◽  
Uniform Distribution ◽  
Sequence Algebra ◽  
Image Position ◽  
Summability Matrix ◽  
Uniform Distribution Of Sequences ◽  
Regular Summability

If A = {am,n} is a regular summability matrix, the sequence s = {sn} is said to be A uniformly distributed (see L. Kuipers, H. Niederreiter, Uniform distribution of sequences, p. 221, John Wiley & Sons, New York, London, Sydney, Toronto, 1974), if(h = 1, 2, …). In this paper we examine sequences belonging to A*, where t ∈ A* if and only if t is bounded and s + t is A uniformly distributed whenever s is A uniformly distributed. By A′ are denoted those members t of A* such that at ∈ A* for every real a. The members of A′ form a Banach algebra, A* is not connected under the sup norm, but A′ is a component.

scholarly journals TheT-statistically convergent sequences are not anFK-space

1995 ◽  
Vol 18 (4) ◽  
pp. 825-827 ◽  
Author(s):  
Jeannette Kline
Keyword(s):  
Summability Matrix ◽  
Locally Convex ◽  
Regular Summability ◽  
Convergent Sequences

In ths note show that under certain restrictions on a nonnegative regular summability matrixT, the space ofT-statistically convergent sequences cannot be endowed with locally convexFKtopology.

Inclusion sets of regular summability matrices. III

1966 ◽  
Vol 62 (3) ◽  
pp. 389-394 ◽  
Author(s):  
J. W. Baker ◽  
G. M. Petersen
Keyword(s):  
Bounded Sequence ◽  
Finite Set ◽  
Summability Matrices ◽  
Image Position ◽  
Summability Matrix ◽  
Regular Summability ◽  
Bounded Sequences

Let A = (am, n) be a (regular summability) matrix. Then will denote the set of bounded sequences which are summed by A. If {Ai} (i = 1, 2, …, N) is a finite set of such matrices, and if consists of every bounded sequence then we shall say that the matrices span the bounded sequences. Ifx = {xn} belongs to then we denote the value to which A sums x by A-lim x. If y = {yn} is any sequence, then the A-transform of y (if it exists) is the sequence {Aμ(y)}, where

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