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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A functional equation arising from ranked additive and separable utility
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by János Aczél, Gyula Maksa, Che Tat Ng and Zsolt Páles PDF
Proc. Amer. Math. Soc. 129 (2001), 989-998 Request permission

Abstract:

All strictly monotonic solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.
References
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Additional Information
  • János Aczél
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • Address at time of publication: Institute for Mathematical Behavioral Sciences, University of California, Irvine, California 92697-5100
  • Email: jdaczel@math.uwaterloo.ca, janos@aris.ss.uci.edu
  • Gyula Maksa
  • Affiliation: Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
  • Email: maksa@math.klte.hu
  • Che Tat Ng
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • Email: ctng@math.uwaterloo.ca
  • Zsolt Páles
  • Affiliation: Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
  • Email: pales@math.klte.hu
  • Received by editor(s): June 7, 1999
  • Published electronically: October 4, 2000
  • Additional Notes: This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada Grants OGP 0002972 and OGP 0008212, by the Hungarian National Science Foundation (OTKA) Grant T-030082 and by the Higher Education Research Council (FKFP) Grant 0310/1997.
    The authors are grateful to R. Duncan Luce for communicating the problem and explanations and to the referee for pointing out a confusing misprint in the first version of the manuscript.
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 989-998
  • MSC (2000): Primary 39B12, 39B22, 39B72; Secondary 26A48, 26A51, 91A30, 91C05
  • DOI: https://doi.org/10.1090/S0002-9939-00-05686-0
  • MathSciNet review: 1814138