Converse Theorems for the Cesàro Summability of Improper Integrals
Yıl 2020,
Cilt: 24 Sayı: 1, 45 - 48, 01.02.2020
Sefa Anıl Sezer
,
Rahmet Savaş
Öz
In this
paper we prove converse theorems to obtain usual convergence of improper
integrals from Cesàro summability.
Kaynakça
- 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.
Yıl 2020,
Cilt: 24 Sayı: 1, 45 - 48, 01.02.2020
Sefa Anıl Sezer
,
Rahmet Savaş
Kaynakça
- 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.