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On Some Triangular Summability Methods
American Journal of Mathematics, 1947It is to be noted that Bn (x) is defined by taking the first n + 1 terms of the series defining the function *J(x) ; the summability method is then constructed with the sequence {x.n}. As set forth in the aforementioned paper of Szasz,2 the regularity of either method (1. 1) or (1. 2) does not imply the regularity of the other method. On the other hand,
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On the Summability of Series by a Method of Valiron
Proceedings of the Edinburgh Mathematical Society, 1936The method of summability with which I shall be concerned here is denoted by (V, α ) and is defined as follows:—The series Σαn is said to be summable (V, α ) to the sum s ifThis is a particular case of a method due to Valiron in which μ–2α is replaced by a function of μ.
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ERGODIC THEOREMS AND SUMMABILITY METHODS
The Quarterly Journal of Mathematics, 1987Given: a regular summation method \((a_{n,m})_{n,m}\) such that \(\sum^{\infty}_{k=m}| a_{n,m+1}-a_{n,m}| \to 0\) uniformly in n and a sequence \((T_ n)_ n\) of bounded operators, chosen independently on a Banach space X. The author investigates conditions under which \(\lim_{n\to \infty}\sum^{\infty}_{m=1}a_{n,m}T_ m,...,T_ 1(x)\) (x\(\in X)\) exists ...
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Summability Methods in Perturbation Theory
Journal of Mathematical Physics, 1970The Mittag-Leffler summability method is applied to operator-valued analytic functions and a corresponding procedure for perturbation theory is derived, which has a bigger region of convergence. This region is explicitly described.
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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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General Summability Methods in the Approximation by Bernstein–Chlodovsky Operators
Numerical Functional Analysis and Optimization, 2021Meryem Ece Alemdar, Oktay Duman
exaly
On the General Methods of Summability
Journal of the London Mathematical Society, 1970openaire +1 more source
A Logarithmic Method of Summability
Journal of the London Mathematical Society, 1958openaire +2 more sources