On the rate of convergence of Ces\`aro means of double Fourier series of functions of generalized bounded variation
Čebyševskij sbornik, Tome 24 (2023) no. 2, pp. 38-62
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In this paper, the rate of convergence of Cesàro means of the double Fourier series of a $2\pi$-periodic function in each variable and of generalized bounded variation, is estimated. The result obtained is a generalization of a result of S. M. Mazhar for a single Fourier series and of our earlier result for a function of two variables.
Keywords:
double Fourier series, generalized bounded variation, pointwise convergence, rate of convergence, Cesàro mean.
@article{CHEB_2023_24_2_a2,
author = {R. K. Bera and B. L. Ghodadra},
title = {On the rate of convergence of {Ces\`aro} means of double {Fourier} series of functions of generalized bounded variation},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {38--62},
publisher = {mathdoc},
volume = {24},
number = {2},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_2_a2/}
}
TY - JOUR AU - R. K. Bera AU - B. L. Ghodadra TI - On the rate of convergence of Ces\`aro means of double Fourier series of functions of generalized bounded variation JO - Čebyševskij sbornik PY - 2023 SP - 38 EP - 62 VL - 24 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHEB_2023_24_2_a2/ LA - en ID - CHEB_2023_24_2_a2 ER -
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R. K. Bera; B. L. Ghodadra. On the rate of convergence of Ces\`aro means of double Fourier series of functions of generalized bounded variation. Čebyševskij sbornik, Tome 24 (2023) no. 2, pp. 38-62. http://geodesic.mathdoc.fr/item/CHEB_2023_24_2_a2/