A few remarks on divergent sequences: rates of divergence. (English) Zbl 1196.40001
In a series of papers published recently the authors demonstrated that there are nice relations between the theory of selection principles (related also to game theory) and the theory of divergent processes in asymptotic analysis [ibid. 327, No. 2, 1297–1306 (2007; Zbl 1116.26002); Note Math. 27, 55–63 (2007); Topology Appl. 155, No. 17–18, 2143–2149 (2008; Zbl 1154.54002); Topology Appl. 156, No. 1, 46–55 (2008; Zbl 1168.54002)].
In this paper the authors define the quotient speed of divergence of a sequence of positive numbers and establish its role in the above study.
[For part II, cf. the authors, ibid. 367, No. 2, 705–709 (2010; Zbl 1196.40002).]
In this paper the authors define the quotient speed of divergence of a sequence of positive numbers and establish its role in the above study.
[For part II, cf. the authors, ibid. 367, No. 2, 705–709 (2010; Zbl 1196.40002).]
Reviewer: S. M. Mazhar (Kuwait)
MSC:
| 40A05 | Convergence and divergence of series and sequences |
Keywords:
regular variation; rapidly varying sequence; quotient speed; selection principles; game theoryReferences:
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