EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 80(94), pp. 241–251 (2006)

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VARIANTS OF KARAMATA'S ITERATION THEOREM

Eugene Seneta

School of Mathematics and Statistics, FO7, University of Sydney, N.S.W. 2006, Australia

Abstract: Karamata's Iteration Theorem is used to refine the asymptotic behavior of iterates of a function, under a more restrictive assumption than Karamata's, but still involving regular variation. A second result gives a necessary and sufficient integral condition for convergence of a series of iterates. Historical background to the idea of regularly varying sequence precedes a short concluding section on attribution of a probabilistic result.

Keywords: iterates, series, convergence, regularly varying sequence, Cauchy integral test, De Morgan, Buniakovsky, domain of attraction, Gnedenko

Classification (MSC2000): 26A12; 40A05; 40-03; 01A55; 01A60

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.

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