• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.263-276
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• 2013

We discuss the effects of the ${\delta}^2$ and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even H$\ddot{o}$lder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1035-1049
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• 2023

Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z^(𝜔)_r)-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.

• Journal for History of Mathematics
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• v.30 no.1
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• pp.17-29
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• 2017

This paper is concerned with the $Ces{\grave{a}}ro$ summability of Fourier series. Many authors have studied on the summability of Fourier series up to now. Also, G. H. Hardy and J. E. Littlewood [5], Gaylord M. Merriman [18], L. S. Bosanquet [1], Fu Traing Wang [24] and others had studied the $Ces{\grave{a}}ro$ summability of Fourier series until the first half of the 20th century. In the section 2, we reintroduce Ernesto $Ces{\grave{a}}ro^{\prime}s$ life and the meaning of mathematical history for $Ces{\grave{a}}ro^{\prime}s$ work. In the section 3, we investigate the classical results of summability for Fourier series from 1897 to the mid-twentieth century. In conclusion, we restate the important classical results of several theorems of $Ces{\grave{a}}ro$ summability for Fourier series. Also, we present the research minor lineage of $Ces{\grave{a}}ro$ summability for Fourier series.