Results 261 to 270 of about 1,040 (304)
Some of the next articles are maybe not open access.
Potent Conservative Summability Methods
Bulletin of the London Mathematical Society, 1994The theorems of this paper are given in a very short form. Before stating them, we need to have some notation and definitions. Notation: \(\chi\) -- the set of all sequences of 0s and 1s; \(K\) -- the set of all conservative matrices; \(T\) -- the set of all thin sequences; \(F\) -- the set of all almost convergent sequences; \((M)\) -- the set of ...
Kuttner, Brian +1 more
openaire +1 more source
ON SOME ABSOLUTE SUMMABILITY METHODS
Analysis, 1987Let \(\Sigma a_ n\) be a given infinite series with sequence of partial sums \(\{s_ n\}\). The series \(\Sigma a_ n\) is said to be summable \(| \bar N,P_ n|_ k,k\geq 1\), if \(\sum^{\infty}_{n=1}(P_ n/p_ n)^{k-1}| t_ n-t_{n-1}|^ k0\), \(P_ n=p_ 0+p_ 1+...+p_ n\to \infty\) and \(t_ n=P_ n^{- 1}\sum^{n}_{\nu =0}p_{\nu}S_{\nu}.\) In the special case when
Bor, H., Thorpe, B.
openaire +2 more sources
Direct Theorems on Methods of Summability
Canadian Journal of Mathematics, 19491.1. A regular Toeplitz method of summability is given by a transformation m = 0, 1, 2 , … of the sequence sn into the sequence σm. According to the definition of regularity, every such method sums a convergent sequence sn to the value lim sn. The question naturally arises, whether there are more extensive classes of sequences summable by all regular
openaire +1 more source
On Riesz and Cesàro methods of summability
Transactions of the American Mathematical Society, 1933* Presented to the Society, December 30, 1931; received by the editors August 24, 1932. t National Research Fellow. t Comptes Rendus, vol. 149 (1909), pp. 18-22. In this note Riesz considered only real positive orders r. ? Comptes Rendus, vol. 152 (1911), pp. 1651-1654. Here again Riesz considered only the case r>O.
openaire +2 more sources
On Borel‐type methods of summability
Mathematika, 1958Suppose throughout that l, a n ( n = 0, 1, …) are arbitrary complex numbers, that α is a fixed positive number and that x is a variable in the interval [0,µ ...
openaire +1 more source
1979
In previous studies we applied Lanzcos' τ-method to get polynomial and rational approximations to series of hypergeometric type. It was shown that the approximations could be viewed as a weighted sum of the partial sums of the given series. This we call a summability method.
openaire +1 more source
In previous studies we applied Lanzcos' τ-method to get polynomial and rational approximations to series of hypergeometric type. It was shown that the approximations could be viewed as a weighted sum of the partial sums of the given series. This we call a summability method.
openaire +1 more source
Scales of Logarithmic Methods of Summability
Canadian Mathematical Bulletin, 1969We suppose throughout that p is a non-negative integer, and use the following notations:where log0x = x for x ≥ e0 = 1, and logn+1x = log(lognx) for x ≥ en+1 = een (n = 0, 1, 2,…);
Borwein, D., Phillips, R.
openaire +1 more source
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,
openaire +2 more sources
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.
openaire +1 more source
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 ...
openaire +2 more sources