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Axiomatisations of the average and a further generalisation of monotonic sequences

  • John Bibby (a1)
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A bounded monotonic sequence is convergent. This paper shows that a bounded sequence which is g-monotonic (to be defined) also converges. The proof generalises one attributed to Professor R. A. Rankin by Copson [1]. The theorem requires two definitions: the first axiomatises the notion of “average“ and the second generalises the concept of monotonicity.

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References
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1.Copson, E. T., On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. 17 (1970), 159164.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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