Real Analysis Exchange

Orders of Growth of Real Functions

Titus Hilberdink

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Abstract

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

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

Dates
First available in Project Euclid: 3 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1199377478

Mathematical Reviews number (MathSciNet)
MR2369850

Zentralblatt MATH identifier
1153.26001

Subjects
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]

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

Citation

Hilberdink, Titus. Orders of Growth of Real Functions. Real Anal. Exchange 32 (2006), no. 2, 359--390. https://projecteuclid.org/euclid.rae/1199377478


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