Abstract

The problem considered is as follows: given C⊂RnC\subset \R^n and F:C→RnF:C\rightarrow \R^n differentiable, find f:C→Rf:C\rightarrow \R differentiable such that ∥∇f(x)∥−1∇f(x)=∥F(x)∥−1F(x)\norm \nabla f(x)\norm^{-1} \nabla f(x) = \norm F(x) \norm^{-1}F(x) for all x∈Cx\in C. Conditions for ff to be pseudoconvex or convex are given. The results are applied to the differentiable case of the revealed preference problem.

Author information

Contact details are reproduced from the original publication and may be historical.

Tamás Rapcsák

Computer and Automation Institute, Hungarian Academy of Sciences, 1518 Budapest, Hungary

Keywords

  • Generalized convexity
  • generalized monotonicity
  • consumer theory
  • direct and indirect utility functions
  • revealed preference theory

Mathematics Subject Classification

90A40, 90C26; 52A41, 47N10, 47H05

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Suggested citation

J.-P. Crouzeix, T. Rapcsák. “Integrability of Pseudomonotone Differentiable Maps and the Revealed Preference Problem.” Journal of Convex Analysis 12 (2005), No. 2, 431–446. https://doi.org/10.68381/jca12030

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.