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On a parameterized system of nonlinear equations with economic applications

Talman,A.J.J.
; 
Yang,Z.F.
Abstract
We study a parameterized system of nonlinear equations. Given a nonempty, compact, and convex set, an affine function, and a point-to-set mapping from the set to the Euclidean space containing the set, we constructively prove that, under certain (boundary) conditions on the mapping, there exists a connected set of zero points of the mapping, i.e., the origin is an element of the image for every point in the connected set, such that the connected set has a nonempty intersection with both the face at which the affine function is minimized and the face at which that function is maximized. This result generalizes and unifies several well-known existence theorems including Browder’s fixed point theorem and Ky Fan’s coincidence theorem. An economic application with constrained equilibria is also discussed.
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2012
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Tilburg University Research Output Collection
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JOTA154.pdf
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Talman, A J J & Yang, Z F 2012, 'On a parameterized system of nonlinear equations with economic applications', Journal of Optimization Theory and Applications, vol. 154, no. 2, pp. 644-671. < http://www.springerlink.com/content/f52w251j13167228/ >
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https://hdl.handle.net/20.500.14602/57785
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info:eu-repo/semantics/restrictedAccess
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