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

VARIANTS OF KARAMATA'S ITERATION THEOREMEugene SenetaSchool of Mathematics and Statistics, FO7, University of Sydney, N.S.W. 2006, AustraliaAbstract: 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; 4003; 01A55; 01A60 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
