Converse Theorems for the Cesàro Summability of Improper Integrals

ISSN: 1301-4048
Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 1997
Yayıncı: Sakarya Üniversitesi Fen Bilimleri Enstitüsü

In this paper we prove converse theorems to obtain usual convergence of improper integrals from Cesàro summability.Keywords: Converse theorem, Tauberian condition, Cesàro summability

PDF

___

[1] İ. Çanak, Ü. Totur, “A Tauberian theorem for Cesàro summability of integrals,” Appl. Math. Lett., vol. 24 no. 3, pp. 391–395, 2011.
[2] İ. Çanak, Ü. Totur, “Tauberian conditions for Cesàro summability of integrals,” Appl. Math. Lett., vol. 24 no. 6, pp. 891–896, 2011. [ 3] İ. Çanak, Ü. Totur, “Tauberian conditions for the ( , ) C  integrability of functions,” Positivity, vol. 21 no. 1, pp. 73–83, 2017.
[4] G. H. Hardy, “Divergent Series,” Clarendon Press, Oxford, 1949.
[5] A. Laforgia, “A theory of divergent integrals,” Appl. Math. Lett., vol. 22 no. 6, pp. 834–840, 2009.
[6] F. Móricz, Z. Németh, “Tauberian conditions under which convergence of integrals follows from summability ( ,1) C over ,” Anal. Math., vol. 26, no. 1, pp. 53–61, 2000.
[7] 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.