Necessary conditions for absolute double matrix summability factors

We obtain necessary conditions for a doubly triangular matrix A to have the property that a double series ΣΣ λ _mn b _mn is summable |A| _k whenever the series ΣΣb _mn is bounded |A| _k .     

On generalized absolute summability factors

In this paper, a general theorem on _|A,δ|k${|A,\delta |}_k$-summability factors which generalize a theorem of Sava? [E. Sava?, On a recent result on absolute summability factors, Appl. Math. Lett. 18 (2005) 1273–1280] on _|A|k${\left|A\right|}_k$-summability factors has been proved.     

On parallel summability of matrices

It is shown that the generalized inverses characterize the parallel sum. The almost positive definite (a.p.d.) matrices introduced by Duffin and Morley [2] are of two types, whose intersection is the class of quasi-positive-definite matrices (Mitra and Puri [7]). The a.p.d. matrices of any one type form a “saturated” subclass of pairwise parallel summable a.p.d. matrices.     

Conditions for the absolute summability in power p of double series

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 46, pp. 112–117, 1986.     

On the absolute summability of trigonometric series

{_n} a _{n n} , s _n n- , _n -n- (, 1)- . . . -, . , «|s₂n+1–s ₂ n¦< . .» «¦ _n – _n–1¦< . .» . s. , {a _n } 0, a _n/n<, {a _n } , {it|_n¦<. , , -.     

On absolute summability factors of infinite series

In this paper using δ-quasi-monotone sequences a theorem on summability factors of infinite series, which generalizes a theorem of Bor [4] on summability factors of infinite series, is proved. Also, in the special case this theorem includes a result of Mazhar [8] on |C, 1|_k summability factors.     

On the generalized absolute summability factor theorem

In this paper, we establish a summability factor theorem for summability _|A|k${\left|A\right|}_k$ where A$A$ is a lower triangular matrix with non-negative entries satisfying certain conditions.     

On generalized absolute Cesàro summability

In this paper, a known result on ∣C, α; δ∣_k summability factors has been generalized for ∣C, α, γ; δ∣_k summability factors. Some new results have also been obtained.     

Tauberian theorems for absolute summability

Ohne ZusammenfassungHerrn A.Ostrowski zum 60. Geburtstag gewidmetThis work has been completed while the author held a Fellowship at the Summer Research Institute of 1952 of the Canadian Mathematical Congress.     

On a recent result on absolute summability factors

In this paper, a general theorem of ${\left|A\right|}_k$ summability factors is presented. This generalization is accomplished by replacing the weighted mean matrix in Mazhar’s theorem in [S.M. Mazhar, A remark on a recent result on absolute summability factors, Indian J. Math. 40 (2) (1998) 123–131] with a triangular matrix.     

Some inclusion theorems for absolute summability

In this work the inclusion relations between absolute summability domains of a normal matrix A and certain factorable matrices are described. Thus, some classes of factorable matrices transforming the absolute summability domain of A into a set of convergent or absolutely convergent series are characterized. As an application, the special case where A is the Cesàro matrix is considered.