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
DOI: https://doi.org/10.18514/MMN.2018.2233


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