Real Analysis Exchange

Orders of Growth of Real Functions

Titus Hilberdink

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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.

Article information

Real Anal. Exchange, Volume 32, Number 2 (2006), 359-390.

First available in Project Euclid: 3 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]
Secondary: 39B12: Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]

Rates of growth of functions orders of infinity Abel functional equation Fractional iteratio


Hilberdink, Titus. Orders of Growth of Real Functions. Real Anal. Exchange 32 (2006), no. 2, 359--390.

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