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On two absolute matrix summability methods
Bollettino dell'Unione Matematica Italiana, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Matrix transformations of summability domains of generalized matrix methods in Banach spaces
Rendiconti del Circolo Matematico di Palermo, 2009The necessary and sufficient conditions for a matrix M to be a transform from the summability domain of generalized matrix method A into the summability domain of another generalized matrix method B are proved. The elements of Mare continuous linear operators from a Banach space X into another Banach space Y, and the elements of A and B are continuous ...
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Submethods Of Regular Matrix Summability Methods
Canadian Journal of Mathematics, 1956By a submethod of a regular matrix method A we mean a method (see 1 or 3) whose matrix is obtained by deleting a set of rows from the matrix A. We establish a one-one correspondence between the submethods of A and the points of the interval 0 < ξ ≤We designate the submethod which corresponds to 𝞷 by A (𝞷) and are accordingly able to speak of sets of
Goffman, Casper, Petersen, G. M.
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Summability Methods on Matrix Spaces
Canadian Journal of Mathematics, 1961The matrix spaces under consideration are the four main types of irreducible bounded symmetric domains given by Cartan (5). Let z = (zjk) be a matrix of complex numbers, z' its transpose, z* its conjugate transpose and I = I(n) the identity matrix of order n.
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Necessary conditions for absolute matrix summability methods
Bollettino dell'Unione Matematica Italiana, 2015The authors obtain necessary conditions in order that a series \(\sum a_{n}\) should be summable \(|B,q_{n}|_{k}\) whenever \(\sum a_{n}\) is summable \( |A,p_{n}|_{k}\) as a generalization of the result of \textit{H. Bor} and \textit{B. Thorpe} [Analysis 12, No. 1--2, 1--3 (1992; Zbl 0753.40007)].
Ozgen, H. N., ÖZARSLAN, HİKMET
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ON SOME NEW INVARIANT MATRIX METHODS OF SUMMABILITY
The Quarterly Journal of Mathematics, 1983Let \(\sigma\) be a mapping of the set of positive integers into itself. A continuous linear functional \(\phi\) on the space \(\ell^{\infty}\) of real bounded sequences is a \(\sigma\)-mean if \(\phi(x)\geq 0\) when the sequence \(x=(x_ n)\) has \(x_ n\geq 0\) for all n, \(\phi(e)=1\) where \(e:=(1,1,...)\), and \(\phi((x_{\sigma(n)}))=\phi(x)\) for ...
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A Theorem on General Matrix Summability Method
Asian Journal of Mathematics and Computer ResearchThis paper establishes a general summability factor theorem for the ϕ − |B; δ|k summability of an infinite series associated with a positive normal matrix B. The study considers the sequence of partial sums of an infinite series and the corresponding matrix transformation determined by B.
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Matrix summability methods on the approximation of multivariate \(q\)-MKZ operators
2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Duman, Oktay +2 more
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Four dimensional matrix characterization P-convergence fields of summability methods
Applied Mathematics and Computation, 2013In 1945 Agnew presented two dimensional matrix characterization of convergent fields. The goal of this paper is to present four dimensional matrix characterization of P-convergent field. This will be accomplished by the presentation of the following multiple dimensional analogues of Agnew's theorem.
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Strong summability of double series by matrix methods and Tauberian theorems for these methods
Mathematical Notes of the Academy of Sciences of the USSR, 1975Conditions are established under which matrix transformations of double series and sequences preserve strong convergence. In addition, a general Tauberian theorem is established and applied to the method of Borel.
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