Summary
Recent applications of functional equations to questions of allocation, aggregation, utility, taxation, theories of measurement and dimensional analysis are discussed and open problems formulated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aczél, J., Ng, C. T., andWagner C.,Aggregation theorems for allocation problems. SIAM J. Algebraic Discrete Methods5 (1984), 1–8.
Buhl, U. H. andPfingsten, A.,Eigenschaften und Verfahren für einenangemessenen Länderfinanzausgleich in der Bundersrepublik Deutschland. Finanzarchiv44 (1) (1986), 98–109.
Aczél, J. andPfingsten, A.,Constituent-sensitive public fund sharing. In Mathematical modelling in economics. Springer, Berlin, 1993, pp. 3–10.
Pokropp, F.,Aggregation von Produktionsfunktionen. Klein-Nataf-Aggregation ohne Annahmen über die Differenzierbarkeit und Stetigkeit. [Lecture Notes in Econom. and Math. Systems, No. 74]. Springer, Berlin, 1972.
van Daal, J. andMerkies, A. H. Q. M.,Consistency and representativity in a historical perspective. InMeasurement in economics. Physica, Heidelberg, 1987, pp. 607–637.
Aczél, J.,A short course on functional equations based upon recent applications to the social and behavioral sciences. Reidel (Kluwer), Dordrecht-Boston, 1987.
Nikodem, K.,The stability of the Pexider equation. Ann. Math. Sil.5 (1991), 91–93.
Chmieliński, J. andTabor, J.,On approximate solutions of the Pexider equations. Aequationes Math.46 (1993).
Marley, A. A. J.,A selective review of recent characterizations of stochastic choice models using distribution and functional equation techniques. Math. Social Sci.23 (1992), 5–29.
Bossert, W.,On intra- and interpersonal utility comparisons. Soc. Choice Welf.8 (1991), 207–219.
Roberts, F. S.,Merging relative scores. J. Math. Anal. Appl.147 (1990), 30–52.
Aczél, J.,Determining merged relative scores. J. Math. Anal. Appl.150 (1990), 20–40.
Young, H. P.,Progressive taxation and the equal sacrifice principle. J. Public Econom.32 (1987), 203–214.
Cohen, M. andNarens, L.,Fundamental unit structures: a theory of ratio scalability. J. Math. Psych.20 (1979), 193–232.
Luce, R. D.,Rank dependent subjective expected-utility representations. J. Risk Uncert.1 (1988), 305–332.
Luce, R. D. andNarens, L.,Classification of concatenation structures by scale types. J. Math. Psych.29 (1985), 1–72.
Narens, L.,A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision13 (1987), 1–70.
Aczél, J.,Three problems. InGeneral inequalities 6. Birkhäuser, Basel-Boston-Berlin, 1992, p. 477.
Aczél, J., Gronau, D., andSchwaiger, J.,Increasing solutions of the homogeneity equation and of similar equations. J. Math. Anal. Appl.182 (1994), 436–464.
Aczél, J., Roberts, F. S., andRosenbaum, Z.,On scientific laws without dimensional constants. J. Math. Anal. Appl.119 (1986), 389–416.
Moszner, Z.,Une généralisation d'un résultat de J. Aczél et M. Hosszú sur l'équation de translation. Aequationes Math.37 (1989), 267–278.
Moszner, Z.,Sur une forme de la solution de l'équation de translation. C.R. Math. Rep. Acad. Sci. Canada12 (1991), 285–290.
Förg-Rob, W.,Differentiable solutions of the translation equation. [Grazer Math. Ber., No. 287]. Karl-Franzens Univ., Graz, 1988.
Aczél, J. andMoszner, Z.,New results on “scale” and “size” arguments justifying invariance properties of empirical indices and laws. Math. Social Sci.28 (1994), 3–33.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aczél, J. Some recent applications of functional equations to the social and behavioral sciences. Further problems. Aeq. Math. 50, 38–49 (1995). https://doi.org/10.1007/BF01831112
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01831112