# Divergent series

(redirected from Summability method)
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Related to Summability method: Convergent series, diverges
Translations
divergentni red
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Recently the Abel method, a nonmatrix summability method, has been used in the Korovkin type approximation of functions in the weighted space (see [4], [5]).
This is a summability method associated with a Riesz matrix which is defined as follows.
k,l]) denotes a four dimensional summability method that maps the complex double sequences x into the double sequence Ax where the k, l-th term to Ax is as follows:
On the other hand, we comment that the study of polynomials related with the Fejer kernel and the study of modifications of the Fejer summability method are currently active research areas; see [2] and [11], respectively.
A general summability method, the so called [theta]-summability is considered for Gabor series.
where T is an arbitrary nonnegative regular matrix summability method [6,8].
linear summability method is also a local property of the generating function f.
k,l]) denote a four dimensional summability method that maps the complex double sequences x into the double sequence Ax where the k, i- th term to Ax is as follows:
u[right arrow][infinity]]y(u) = s exists, we say that x = x(u) is convergent to s with respect to the summability method A (or x is summable to s by the method A) and write x(u) [right arrow] s(A).
A general summability method, the so-called [theta]-summability, is considered for Gabor series.
Quite recently, several new Tauberian conditions for (A) (C, [alpha]) summability method have been obtained in Canak et al.
We obtain a summability method that maps the double complex sequence w into the double complex sequence Aw where the mnth term of Aw is as follows:
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