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\(I\)-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.

MSC:

40A35 Ideal and statistical convergence
40D09 Structure of summability fields
40D20 Summability and bounded fields of methods

Citations:

Zbl 1110.40002
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