• Journal of the Korean Mathematical Society
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• v.15 no.2
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• pp.167-176
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• 1979

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.57-68
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• 2016

In this work, we shall give the degree of approximation for functions belonging to $H{\ddot{o}}lder$ class by matrix summability method of multiple Fourier series in the $H{\ddot{o}}lder$ metric.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.321-332
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• 2015

This paper is concerned with the convergence of double trigonometric series and Fourier series. Since the beginning of the 20th century, many authors have studied on those series. Also, Ferenc $M{\acute{o}}ricz$ has studied the convergence of double trigonometric series and double Fourier series so far. We consider $L^p(T^2)$-convergence results focused on the Ferenc $M{\acute{o}}ricz^{\prime}s$ studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc $M{\acute{o}}ricz^{\prime}s$ remarkable theorems. Also we investigate his several important results. In conclusion, we investigate his research trends and the simple minor genealogy from J. B. Joseph Fourier to Ferenc $M{\acute{o}}ricz$. In addition, we present the research minor lineage of his study on $L^p(T^2)$-convergence.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.115-124
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• 2006

Functions of bounded variation were discovered by Jordan in 1881 while working out the proof of Dirichlet concerning the convergence of Fourier series. Here, we investigate Waterman's study with respect to bounded variation and its application on a closed bounded interval. The value of his study is whether Dirichlet-Jordan theorem holds in which function classes or not and summability method is what modifies its Fourier coefficients to make resulting series converge to the associated function. We have a view that the directions of future research with respect to bounded variation are two things; one is to find the function spaces which are larger than HBV and smaller than ${\phi}BV$, and the other is to find a fields of applications.