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Volume 31, Issue 3
Readjustment of the Paper [J. Kaur and S. S. Bhatia, Integrability and $L^1$-Convergence of Double Cosine Trigonometric Series, Anal. Theory Appl., 27(1) (2011), pp. 32-39]

Xh. Z. Krasniqi

DOI: 10.4208/ata.2015.v31.n3.7

Anal. Theory Appl., 31 (2015), pp. 299-306.

Published online: 2017-07

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  • Abstract

In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences $J_d$ introduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class $J_d$ usable considering a particular double cosine trigonometric series.

  • Keywords

$L^1$-convergence, double null sequence, cosine trigonometric series, modified sums.

  • AMS Subject Headings

42A20, 42B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-299, author = {Xh. Z. Krasniqi}, title = {Readjustment of the Paper [J. Kaur and S. S. Bhatia, Integrability and $L^1$-Convergence of Double Cosine Trigonometric Series, Anal. Theory Appl., 27(1) (2011), pp. 32-39]}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {3}, pages = {299--306}, abstract = {

In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences $J_d$ introduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class $J_d$ usable considering a particular double cosine trigonometric series.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n3.7}, url = {http://global-sci.org/intro/article_detail/ata/4641.html} }
TY - JOUR T1 - Readjustment of the Paper [J. Kaur and S. S. Bhatia, Integrability and $L^1$-Convergence of Double Cosine Trigonometric Series, Anal. Theory Appl., 27(1) (2011), pp. 32-39] AU - Xh. Z. Krasniqi JO - Analysis in Theory and Applications VL - 3 SP - 299 EP - 306 PY - 2017 DA - 2017/07 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n3.7 UR - https://global-sci.org/intro/article_detail/ata/4641.html KW - $L^1$-convergence, double null sequence, cosine trigonometric series, modified sums. AB -

In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences $J_d$ introduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class $J_d$ usable considering a particular double cosine trigonometric series.

Xh. Z. Krasniqi. (2017). Readjustment of the Paper [J. Kaur and S. S. Bhatia, Integrability and $L^1$-Convergence of Double Cosine Trigonometric Series, Anal. Theory Appl., 27(1) (2011), pp. 32-39]. Analysis in Theory and Applications. 31 (3). 299-306. doi:10.4208/ata.2015.v31.n3.7
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