Book Volume 3 1987

A Short Course on Functional Equations

Based Upon Recent Applications to the Social and Behavioral Sciences

Authors:

ISBN: 978-90-277-2377-2 (Print) 978-94-009-3749-9 (Online)

Table of contents (9 chapters)

  1. Front Matter

    Pages i-vi

  2. No Access

    Chapter

    Pages 1-1

    Introduction

  3. No Access

    Chapter

    Pages 2-21

    An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions.Two extension theorems

  4. No Access

    Chapter

    Pages 22-34

    Scale-invariant equal sacrifice in taxation. The linear-affine functional equation. Multiplicative and logarithmic functions

  5. No Access

    Chapter

    Pages 35-51

    General forms of ‘laws of science’ without dimensional constants. The case of the same ratio scale for all variables. Generalized homogeneous functions. Inequality measures

  6. No Access

    Chapter

    Pages 52-70

    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

  7. No Access

    Chapter

    Pages 71-91

    Pexider’s equation and its extension. Quasi-extension of Cauchy’s equation. Determination of all generalized Hicks-neutral production functions

  8. No Access

    Chapter

    Pages 92-105

    Determination of all Hicks-neutral production functions depending upon capital, labor and time (state of technology). The translation equation

  9. No Access

    Chapter

    Pages 106-132

    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

  10. No Access

    Chapter

    Pages 133-153

    Synthesis of measure judgements. Equations in a single variable. The Abel and Schröder equations. Iteration

  11. Back Matter

    Pages 155-169