# Cesáro summation

(redirected from Cesaro mean)

## Cesáro summation

[chā′zä·rō sə′mā·shən]
(mathematics)
A method of attaching sums to certain divergent sequences and series by taking averages of the first n terms and passing to the limit.
References in periodicals archive ?
The nth Cesaro mean of type (b - 1, c) of f(z) [member of] [A.sub.0] is given by
which is the Cesaro mean of order [delta] for [delta] > -1.
A generalization of Orlicz sequence spaces by Cesaro mean of order one.
We define the kth order Cesaro mean by the following formula:
It is clear that the first order Cesaro mean [Ces.sup.(n).sub.1](x, V) is nothing but (1/n)[[SIGMA].sup.n-1.sub.i=0][V.sup.i](x).
The relation between Cesaro mean and Fejer mean is given by
In sequel, Alexits  studied the degree of approximation of the functions in [H.sub.[alpha]] class by the Cesaro means of their Fourier series in the sup-norm.
Maddox, A new type of Cesaro mean, Analysis, 9 (1989), no.
For the sequence ([[sigma].sub.k](0)) of Cesaro means of order one of the sequence (d(0, [A.sub.k])) we have
This classical theorem states that for 2[pi]-periodic continuous functions f (x) the sequence of Cesaro means {[[sigma].sub.N]} of the partial sums of the Fourier series of f (x) converges uniformly to f (x) on [-[pi], [pi]].
We denote by [u.sub.n.sup.[alpha]] and [t.sub.n.sup.[alpha]] the n-th Cesaro means of order [alpha], with [alpha] > -1, of the sequence ([s.sub.n]) and ([na.sub.n]), respectively, i.e.,
We denote by [u.sup.[alpha][beta].sub.n] and [t.sup.[alpha][beta].sub.n] the nth Cesaro means of order ([alpha], [beta]), with [alpha] + [beta] > -1, of the sequence ([s.sub.n]) and ([na.sub.n)], respectively, i.e., (see )
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