Open Access
2006/2007 Orders of Growth of Real Functions
Titus Hilberdink
Real Anal. Exchange 32(2): 359-390 (2006/2007).


In this paper we define the notion of order of a function, which measures its growth rate with respect to a given function. We introduce the notions of continuity and linearity at infinity with which we characterize order-comparability and equivalence. Using the theory we have developed, we apply orders of functions to give a simple and natural criterion for the uniqueness of fractional and continuous iterates of a function.


Download Citation

Titus Hilberdink. "Orders of Growth of Real Functions." Real Anal. Exchange 32 (2) 359 - 390, 2006/2007.


Published: 2006/2007
First available in Project Euclid: 3 January 2008

zbMATH: 1153.26001
MathSciNet: MR2369850

Primary: 26A12
Secondary: 39B12

Keywords: Abel functional equation , Fractional iteratio , orders of infinity , Rates of growth of functions

Rights: Copyright © 2006 Michigan State University Press

Vol.32 • No. 2 • 2006/2007
Back to Top