Some Tauberian theorems for weighted means of double integrals
Let p(x) and q(y) be nondecreasing continuous functions on [0,∞) such that p(0)=q(0)=0 and p(x),q(y)→∞ as x,y→∞. For a locally integrable function f(x,y) on R₊²=[0,∞)×[0,∞), we denote its double integral by F(x,y)=∫₀^{x}∫₀^{y}f(t,s)dtds and its weighted mean of type (α,β) by
Keywords:
Divergent integrals weighted means of double integrals, Tauberian theorems and conditions,
___
- Çanak, İ. and Totur, Ü., The (C,α) integrability of functions by weighted mean method, Filomat. 26(6) (2012), 1209-1214.
- Çanak, İ., Totur, Ü. and Sezer, S. A., Cesàro integrability and Tauberian theorems in quantum calculus, An. Ştiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 64(1) (2018), 9-19.
- Çanak, İ. and Totur, Ü., On the Cesàro summability for function of two variables, Miskolc Math. Notes., 19(2) (2018), 1203-1215.
- Fındık, G. and Çanak, İ., Some Tauberian theorems for weighted means of double integrals, Paper presented at the 2nd International Conference of Mathematical Sciences (ICMS 2018), 31 July 2018-06 August 2018, Maltepe University, İstanbul, Turkey.
- Fitouhi, A. and Brahim, K., Tauberian theorems in quantum calculus, J. Nonlinear Math. Phys. 14 (2007), 324-330.
- Laforgia, A., A theory of divergent integrals, Appl. Math. Lett. 22 (2009), 834-840.
- Móricz, F., Tauberian theorems for Cesàro summable double integrals over R²₊, Stud. Math. 138(1) (2000), 41-52.
- Özsaraç, F. and Çanak, İ., Tauberian theorems for iterations of weighted mean summable integrals, Positivity (forthcoming). doi.org/10.1007/s11117-018-0603-4.
- Totur, Ü., Okur, M. A. and Çanak, İ. One-sided conditions for the (N, p) summability of integrals, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 80(3) (2018), 65-74.
- Totur, Ü. and Çanak, İ., General Tauberian theorems for Cesàro integrability of functions, Georgian Math. (forthcoming). doi.org/10.1515/gmj-2019-2005.
- Totur, Ü., Çanak, İ. and Sezer, S. A., Weighted integrability and its applications in quantum calculus, Proc. Nat. Acad. Sci. India Sect. A. doi.org/10.1007/s40010-018-0537-z.
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi
Sayıdaki Diğer Makaleler
Ekrem SAVAŞ, Ulas YAMANCİ, Mehmet GÜRDAL
K. MEENA, D. ARİVUOLİ, K. SİVAKAMASUNDARİ
R. Vimal KUMAR, D. VİJAYALAKSHMİ
Convergence of solutions of nonautonomous Nicholson's Blowflies model with impulses
On equitable chromatic number of Tadpole graph T_{m,n}