\(I\)-monotonic and \(I\)-convergent sequences. (English) Zbl 1232.40001
The authors address the notion of \(I\)-monotonic sequences. They obtain the decomposition theorem based on the definition of T. Šalát, B. C. Tripathy and M. Ziman [Tatra Mt. Math. Publ. 28, No. 2, 279–286 (2004; Zbl 1110.40002)] and extend some results on such sequences. Moreover, the different notions of convergence of series for real or complex numbers is generalized.
Reviewer: Yilmaz Erdem (Aydin)
MSC:
40A35 | Ideal and statistical convergence |
40D09 | Structure of summability fields |
40D20 | Summability and bounded fields of methods |