Authors: Stević, Stevo 
Title: Asymptotic behavior of a sequence defined by iteration with applications
Journal: Colloquium Mathematicum
Volume: 93
Issue: 2
First page: 267
Last page: 276
Issue Date: 1-Jan-2002
ISSN: 0010-1354
DOI: 10.4064/cm93-2-6
Abstract: 
We consider the asymptotic behavior of some classes of sequences defined by a recurrent formula. The main result is the following: Let f: (0, ∞)2 → (0, ∞) be a continuous function such that (a) 0 < f(x, y) < px + (1 - p)y for some p ε (0, 1) and for all x, y ε (0, α), where (formula prsented) uniformly in a neighborhood of the origin, where (formula prsented). Then the sequence (xn) satisfies the following asymptotic formula: (formula prsented).
Keywords: Asymptotic behavior | Homogeneous polynomial | Origin | Sequence, difference equation
Publisher: Instytut Matematyczny Polskiej Akademii Nauk

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