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A Short Course on Functional Equations

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Cover of 'A Short Course on Functional Equations'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions.Two extension theorems
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    Chapter 3 Scale-invariant equal sacrifice in taxation. The linear-affine functional equation. Multiplicative and logarithmic functions
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    Chapter 4 General forms of ‘laws of science’ without dimensional constants. The case of the same ratio scale for all variables. Generalized homogeneous functions. Inequality measures
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    Chapter 5 General forms of ‘laws of sciences’ with (partially) independent ratio and interval scales. Multiplace multiplicative and logarithmic functions. Price levels.Endomorphisms of a real field. The exponential equation. Characters
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    Chapter 6 Pexider’s equation and its extension. Quasi-extension of Cauchy’s equation. Determination of all generalized Hicks-neutral production functions
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    Chapter 7 Determination of all Hicks-neutral production functions depending upon capital, labor and time (state of technology). The translation equation
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    Chapter 8 The associativity equation. Synthesis of ratio judgements. The quasiarithmetic means. The Jensen equations. A conditional linear-affine equation. A characterization of root-mean-powers and of the geometric mean
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    Chapter 9 Synthesis of measure judgements. Equations in a single variable. The Abel and Schröder equations. Iteration
Attention for Chapter 2: An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions.Two extension theorems
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Chapter title
An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions.Two extension theorems
Chapter number 2
Book title
A Short Course on Functional Equations
Published by
Springer, Dordrecht, January 1987
DOI 10.1007/978-94-009-3749-9_2
Book ISBNs
978-9-02-772377-2, 978-9-40-093749-9
Authors

J. Aczél, Aczél, J.

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