Short Course on Functional Equations

• Section 1. An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions. Two extension theorems..- Section 2. Scale-invariant equal sacrifice in taxation. The linear-affine functional equation. Multiplicative and logarithmic functions..- Section 3. General forms of ‘laws of sciences’ without dimensional constants. The case of the same ratio scale for all variables. Generalized homogeneous functions. Inequality measures..- Section 4. General forms of ‘laws of science’ with (partially) independent ratio and interval scales. Multiplace multiplicative and logarithmic functions. Price levels. Endomorphisms of a real field. The exponential equation. Characters..- Section 5. Pexider’s equation and its extension. Quasi-extension of Cauchy’s equation. Determination of all generalized Hicks-neutral production functions..- Section 6. Determination of all Hicks-neutral production functions depending upon capital, labor and time (state of technology). The translation equation..- Section 7. 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..- Section 8. Synthesis of measure judgements. Equations in a single variable. The Abel and Schröder equations. Iteration..- References.- Index of names.

'... this book is not only an impressive example how mathematics can be applied to problems arising in the social and behavioral sciences, but also on outstanding course on functional equations. This course is short, as the title says, but leads astonishingly far, since the material is presented very economically. I am convinced that every reader will enjoy this book greatly.' Zeischrift fur Operations Research, June 1989.