Skip to main content

Some recent applications of functional equations to the social and behavioral sciences. Further problems

  • Chapter
  • 107 Accesses

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.

Keywords

  • Functional Equation
  • Behavioral Science
  • Recent Application
  • Aequationes Math
  • Equalization Payment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-0348-9096-0_4
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   99.00
Price excludes VAT (USA)
  • ISBN: 978-3-0348-9096-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   129.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aczél, J., NG, C. T., and Wagner C., Aggregation theorems for allocation problems. SIAM J. Algebraic Discrete Methods 5 (1984), 1–8.

    MATH  CrossRef  Google Scholar 

  2. Buhl, U. H. and Pfingsten, A., Eigenschaften und Verfahren für einenangemessenen Länderfinanzausgleich in der Bundersrepublik Deutschland. Finanzarchiv 44 (1) (1986), 98–109.

    Google Scholar 

  3. Aczél, J. and Pfingsten, A., Constituent-sensitive public fund sharing. In Mathematical modelling in economics. Springer, Berlin, 1993, pp. 3–10.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. Van Daal, J. and Merkies, A. H. Q. M., Consistency and representativity in a historical perspective. In Measurement in economics. Physica, Heidelberg, 1987, pp. 607–637.

    Google Scholar 

  6. Aczél, J., A short course on functional equations based upon recent applications to the social and behavioral sciences. Reidel ( Kluwer ), Dordrecht-Boston, 1987.

    Google Scholar 

  7. Nikodem, K., The stability of the Pexider equation. Ann. Math. Sil. 5 (1991), 91–93.

    MathSciNet  Google Scholar 

  8. Chmieliński, J. and Tabor, J., On approximate solutions of the Pexider equations. Aequationes Math. 46 (1993).

    Google Scholar 

  9. 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.

    MathSciNet  MATH  CrossRef  Google Scholar 

  10. Bossert, W., On finira-and interpersonal utility comparisons. Soc. Choice Welf. 8 (1991), 207–219.

    MathSciNet  MATH  CrossRef  Google Scholar 

  11. Roberts, F. S., Merging relative scores. J. Math. Anal. Appl. 147 (1990),30–52.

    MathSciNet  MATH  CrossRef  Google Scholar 

  12. Aczél, J., Determining merged relative scores. J. Math. Anal. Appl. 150 (1990), 20–40.

    MathSciNet  MATH  CrossRef  Google Scholar 

  13. Young, H. P., Progressive taxation and the equal sacrifice principle. J. Public Econom. 32 (1987), 203–214.

    CrossRef  Google Scholar 

  14. Cohen, M. and Narens, L., Fundamental unit structures: a theory of ratio scalability. J. Math. Psych. 20 (1979), 193–232.

    MathSciNet  MATH  CrossRef  Google Scholar 

  15. Luce, R. D., Rank dependent subjective expected-utility representations. J. Risk Uncert. 1 (1988), 305–332.

    CrossRef  Google Scholar 

  16. Luce, R. D. and Narens, L., Classification of concatenation structures by scale types. J. Math. Psych. 29 (1985), 1–72.

    MathSciNet  MATH  CrossRef  Google Scholar 

  17. Narens, L., A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision 13 (1987), 1–70.

    MathSciNet  CrossRef  Google Scholar 

  18. Aczél, J., Three problems. In General inequalities 6. Birkhäuser, Basel-Boston-Berlin, 1992, p. 477.

    Google Scholar 

  19. Aczél, J., Gronau, D., and Schwaiger, J., Increasing solutions of the homogeneity equation and of similar equations. J. Math. Anal. Appl. 182 (1994), 436–464.

    MathSciNet  MATH  CrossRef  Google Scholar 

  20. Aczél, J., Roberts, F. S., and Rosenbaum, Z., On scientific laws without dimensional constants. J. Math. Anal. Appt. 119 (1986), 389–416.

    MATH  CrossRef  Google Scholar 

  21. Moszner, Z., Une généralisation d’un résultat de J. Aczél et M. Hosszû sur l’équation de translation. Aequationes Math. 37 (1989), 267–278.

    MathSciNet  MATH  CrossRef  Google Scholar 

  22. Moszner, Z., Sur une forme de la solution de l’équation de translation. C.R. Math. Rep. Acad. Sci. Canada 12 (1991), 285–290.

    MathSciNet  Google Scholar 

  23. Förg-Rob, W., Differentiable solutions of the translation equation. [Grazer Math. Ber., No. 287]. Karl-Franzens Univ., Graz, 1988.

    MATH  Google Scholar 

  24. Aczél, J. and Moszner, Z., New results on “scale” and “size” arguments justifying invariance properties of empirical indices and laws. Math. Social Sci. 28 (1994), 3–33.

    MathSciNet  MATH  CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1995 Birkhäuser Verlag Basel

About this chapter

Cite this chapter

Aczél, J. (1995). Some recent applications of functional equations to the social and behavioral sciences. Further problems. In: Aczél, J. (eds) Aggregating clones, colors, equations, iterates, numbers, and tiles. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9096-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-9096-0_4

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-5243-1

  • Online ISBN: 978-3-0348-9096-0

  • eBook Packages: Springer Book Archive