MMN-2233
Approximation by Nörlund and Riesz type deferred Cesaro means in the space $H^{(\omega)}_{p}$
Ugur Deger; Hilal Bayindir;Abstract
The deferred Ces\'{a}ro transformations which have useful properties
not possessed by the Ces\'{a}ro transformation was considered by
R.P. Agnew in \cite{Agnew}. In \cite{DK}, De\v{g}er and
K\"{u}\c{c}\"{u}kaslan introduced a generalization of deferred
Ces\'{a}ro transformations by taking account of some well known
transformations such as Woronoi-N\"{o}rlund and Riesz, and
considered the degree of approximation by the generalized deferred
Ces\'{a}ro means in the space $H(\alpha,p)$, $p\geq1$,
$0<\alpha\leq1$ by concerning with some sequence classes. In 2014,
Nayak \emph{et al.} studied the rate of convergence problem of
Fourier series by deferred Ces\'{a}ro mean in the space
$H_{p}^{\omega}$ introduced by Das \emph{et al.} in \cite{DNR}.
In this studying, we shall give the degree of approximation by the
generalized deferred Ces\'{a}ro means in the space $H_{p}^{\omega}$.
Therefore the results given in \cite{NDR} are generalized according
to the summability method.
Vol. 19 (2018), No. 2, pp. 823-833