Geodesic
Variants of Karamata's Iteration Theorem
Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 241

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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.
DOI : 10.2298/PIM0694241S
Classification : 26A12 40A05 40-03 01A55 01A60
Keywords: iterates, series, convergence, regularly varying sequence, Cauchy integral test, De Morgan, Buniakovsky, domain of attraction, Gnedenko 
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     author = {Eugene Seneta},
     title = {Variants of {Karamata's} {Iteration} {Theorem}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {241 },
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     zbl = {1246.26004},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0694241S/}
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Eugene Seneta. Variants of Karamata's Iteration Theorem. Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 241 . doi: 10.2298/PIM0694241S

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