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Converse Theorems for the Cesàro Summability of Improper Integrals

Year 2020, Volume: 24 Issue: 1, 45 - 48, 01.02.2020

Sefa Anıl Sezer Rahmet Savaş

https://doi.org/10.16984/saufenbilder.598645

Abstract

In this
paper we prove converse theorems to obtain usual convergence of improper
integrals from Cesàro summability.

Keywords

Converse theorem Tauberian condition

References

  • İ. Çanak, Ü. Totur, “A Tauberian theorem for Cesàro summability of integrals,” Appl. Math. Lett., vol. 24 no. 3, pp. 391–395, 2011.
  • İ. Çanak, Ü. Totur, “Tauberian conditions for Cesàro summability of integrals,” Appl. Math. Lett., vol. 24 no. 6, pp. 891–896, 2011.
  • İ. Çanak, Ü. Totur, “Tauberian conditions for the integrability of functions,” Positivity, vol. 21 no. 1, pp. 73–83, 2017.
  • G. H. Hardy, “Divergent Series,” Clarendon Press, Oxford, 1949.
  • A. Laforgia, “A theory of divergent integrals,” Appl. Math. Lett., vol. 22 no. 6, pp. 834–840, 2009.
  • F. Móricz, Z. Németh, “Tauberian conditions under which convergence of integrals follows from summability over ,” Anal. Math., vol. 26, no. 1, pp. 53–61, 2000.
  • F. Móricz, “Necessary and sufficient Tauberian conditions in the case of weighted mean summable integrals over ,” Math. Inequal. Appl., vol. 7, no. 1, pp. 87–93, 2004.

Year 2020, Volume: 24 Issue: 1, 45 - 48, 01.02.2020

Sefa Anıl Sezer Rahmet Savaş

https://doi.org/10.16984/saufenbilder.598645

Abstract

References

  • İ. Çanak, Ü. Totur, “A Tauberian theorem for Cesàro summability of integrals,” Appl. Math. Lett., vol. 24 no. 3, pp. 391–395, 2011.
  • İ. Çanak, Ü. Totur, “Tauberian conditions for Cesàro summability of integrals,” Appl. Math. Lett., vol. 24 no. 6, pp. 891–896, 2011.
  • İ. Çanak, Ü. Totur, “Tauberian conditions for the integrability of functions,” Positivity, vol. 21 no. 1, pp. 73–83, 2017.
  • G. H. Hardy, “Divergent Series,” Clarendon Press, Oxford, 1949.
  • A. Laforgia, “A theory of divergent integrals,” Appl. Math. Lett., vol. 22 no. 6, pp. 834–840, 2009.
  • F. Móricz, Z. Németh, “Tauberian conditions under which convergence of integrals follows from summability over ,” Anal. Math., vol. 26, no. 1, pp. 53–61, 2000.
  • F. Móricz, “Necessary and sufficient Tauberian conditions in the case of weighted mean summable integrals over ,” Math. Inequal. Appl., vol. 7, no. 1, pp. 87–93, 2004.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Sefa Anıl Sezer 0000-0002-8053-9991

Rahmet Savaş 0000-0002-3670-622X

Publication Date February 1, 2020
Submission Date July 30, 2019
Acceptance Date September 26, 2019
Published in Issue Year 2020 Volume: 24 Issue: 1

Cite

APA Sezer, S. A., & Savaş, R. (2020). Converse Theorems for the Cesàro Summability of Improper Integrals. Sakarya University Journal of Science, 24(1), 45-48. https://doi.org/10.16984/saufenbilder.598645
AMA Sezer SA, Savaş R. Converse Theorems for the Cesàro Summability of Improper Integrals. SAUJS. February 2020;24(1):45-48. doi:10.16984/saufenbilder.598645
Chicago Sezer, Sefa Anıl, and Rahmet Savaş. “Converse Theorems for the Cesàro Summability of Improper Integrals”. Sakarya University Journal of Science 24, no. 1 (February 2020): 45-48. https://doi.org/10.16984/saufenbilder.598645.
EndNote Sezer SA, Savaş R (February 1, 2020) Converse Theorems for the Cesàro Summability of Improper Integrals. Sakarya University Journal of Science 24 1 45–48.
IEEE S. A. Sezer and R. Savaş, “Converse Theorems for the Cesàro Summability of Improper Integrals”, SAUJS, vol. 24, no. 1, pp. 45–48, 2020, doi: 10.16984/saufenbilder.598645.
ISNAD Sezer, Sefa Anıl - Savaş, Rahmet. “Converse Theorems for the Cesàro Summability of Improper Integrals”. Sakarya University Journal of Science 24/1 (February 2020), 45-48. https://doi.org/10.16984/saufenbilder.598645.
JAMA Sezer SA, Savaş R. Converse Theorems for the Cesàro Summability of Improper Integrals. SAUJS. 2020;24:45–48.
MLA Sezer, Sefa Anıl and Rahmet Savaş. “Converse Theorems for the Cesàro Summability of Improper Integrals”. Sakarya University Journal of Science, vol. 24, no. 1, 2020, pp. 45-48, doi:10.16984/saufenbilder.598645.
Vancouver Sezer SA, Savaş R. Converse Theorems for the Cesàro Summability of Improper Integrals. SAUJS. 2020;24(1):45-8.
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